Edit Profile (opens in new tab) Tikhonov, Sergey Yur’evich Co-Author Distance Author ID: tikhonov.sergey-yu Published as: Tikhonov, Sergey; Tikhonov, S. Yu.; Tikhonov, S.; Tikhonov, Sergey Yu.; Tikhonov, Sergeĭ Yur’evich; Tikhonov, Sergei Yu.; Tikhonov, Sergej Yu. more...less Further Spellings: Тихонов Сергей Юрьевич External Links: MGP · Google Scholar · Math-Net.Ru · dblp Documents Indexed: 132 Publications since 2002, including 2 Books and 8 Additional arXiv Preprints 6 Contributions as Editor Co-Authors: 46 Co-Authors with 103 Joint Publications 1,230 Co-Co-Authors all top 5 Co-Authors 23 single-authored 19 Gorbachëv, Dmitriĭ Viktorovich 17 D’yachenko, Mikhaĭl Ivanovich 14 Simonov, Boris Vital’evich 13 Nursultanov, Erlan D. 11 Dai, Feng 9 Liflyand, Elijah 9 Potapov, Mikhaĭl Konstantinovich 8 Ivanov, Valerĭ Ivanovich 8 Temlyakov, Vladimir Nikolaevich 7 Dominguez, Oscar 5 Kolomoitsev, Yurii S. 5 Ruzhansky, Michael V. 4 Ditzian, Zeev 4 Prymak, Andriy V. 3 De Carli, Laura 3 Mukanov, Askhat Birlesovich 3 Saucedo, Miquel 3 Trebels, Walter 2 Ganzburg, Michael Iosifovich 2 Gogatishvili, Amiran 2 Li, Yinqin 2 Opic, Bohumír 2 Stepanov, Vladimir Dmitrievich 2 Tleukhanova, Nazerke Tulekovna 2 Yang, Dachun 2 Yuan, Wen 2 Zeltser, Maria 1 Abell, Martha L. 1 Ash, J. Marshall 1 Belov, Aleksandr S. 1 Bondarenko, Andriy V. 1 Borodin, Petr A. 1 Cruz-Uribe, David Vincente 1 Debernardi Pinos, Alberto 1 Dinh Dũng 1 Erlan, Nursultanov 1 Fedorov, V. M. 1 Feng, Han 1 Fiorenza, Alberto 1 Glazyrina, Polina Yu. 1 Haroske, Dorothee D. 1 Iacob, Emil 1 Kashin, Boris Sergeevich 1 Kolesnikov, Alexander V. 1 Kosov, Egor D. 1 Lomako, Tetiana 1 Lukashenko, Taras P. 1 Mel’nikov, I. I. 1 Mhaskar, Hrushikesh N. 1 Sadovnichiĭ, Viktor Antonovich 1 Skvortsov, Valentin Anatol’evich 1 Solodov, Alekseĭ Petrovich 1 Stëpin, Anatoliĭ Mikhaĭlovich 1 Stokolos, Alex 1 Taylor, Sharon 1 Ullrich, Tino 1 Weisz, Ferenc 1 Wirth, Jens 1 Xu, Yuan 1 Yuditskii, Peter Meerovich 1 Zhu, Jiehua all top 5 Serials 9 Journal of Approximation Theory 7 Journal of Mathematical Analysis and Applications 6 Constructive Approximation 6 The Journal of Fourier Analysis and Applications 4 Mathematical Notes 4 Proceedings of the American Mathematical Society 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Proceedings of the Steklov Institute of Mathematics 4 Advanced Courses in Mathematics – CRM Barcelona 3 Journal d’Analyse Mathématique 3 Moscow University Mathematics Bulletin 3 Russian Mathematical Surveys 3 Studia Mathematica 3 Journal of Functional Analysis 3 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika 3 Calculus of Variations and Partial Differential Equations 2 Canadian Journal of Mathematics 2 Mathematische Zeitschrift 2 Memoirs of the American Mathematical Society 2 Transactions of the American Mathematical Society 2 Acta Mathematica Hungarica 2 Journal of Complexity 2 Revista Matemática Iberoamericana 2 Potential Analysis 2 Bulletin des Sciences Mathématiques 2 Sbornik: Mathematics 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 Applied and Numerical Harmonic Analysis 1 Analysis Mathematica 1 Ukraïns’kyĭ Matematychnyĭ Zhurnal 1 Acta Scientiarum Mathematicarum 1 Functional Analysis and its Applications 1 Indiana University Mathematics Journal 1 Mathematische Nachrichten 1 Mathematica Scandinavica 1 Michigan Mathematical Journal 1 Publications de l’Institut Mathématique. Nouvelle Série 1 Real Analysis Exchange 1 Zeitschrift für Analysis und ihre Anwendungen 1 IMRN. International Mathematics Research Notices 1 The Journal of Geometric Analysis 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Journal on Mathematical Analysis 1 ETNA. Electronic Transactions on Numerical Analysis 1 Izvestiya: Mathematics 1 Doklady Mathematics 1 Mathematical Inequalities & Applications 1 Journal of the European Mathematical Society (JEMS) 1 JIPAM. Journal of Inequalities in Pure & Applied Mathematics 1 Surveys in Approximation Theory (SAT) 1 Complex Variables and Elliptic Equations 1 Jaen Journal on Approximation 1 Eurasian Mathematical Journal 1 Bulletin of Mathematical Sciences 1 Forum of Mathematics, Sigma all top 5 Fields 103 Harmonic analysis on Euclidean spaces (42-XX) 45 Approximations and expansions (41-XX) 44 Functional analysis (46-XX) 39 Real functions (26-XX) 11 Special functions (33-XX) 9 Numerical analysis (65-XX) 7 Integral transforms, operational calculus (44-XX) 5 Partial differential equations (35-XX) 5 Operator theory (47-XX) 4 Sequences, series, summability (40-XX) 3 General and overarching topics; collections (00-XX) 2 Functions of a complex variable (30-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral equations (45-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 114 Publications have been cited 1,367 times in 594 Documents Cited by ▼ Year ▼ Hyperbolic cross approximation. Lecture notes given at the courses on constructive approximation and harmonic analysis, Barcelona, Spain, May 30 – June 3, 2016. Zbl 1414.41001 Dũng, Dinh; Temlyakov, Vladimir; Ullrich, Tino 97 2018 Trigonometric series with general monotone coefficients. Zbl 1106.42003 Tikhonov, S. 86 2007 Ul’yanov and Nikol’skii-type inequalities. Zbl 1069.41014 Ditzian, Z.; Tikhonov, S. 47 2005 Pitt’s inequalities and uncertainty principle for generalized Fourier transform. Zbl 1404.42019 Gorbachev, Dmitry V.; Ivanov, Valerii I.; Tikhonov, Sergey Yu. 47 2016 A concept of general monotonicity and applications. Zbl 1223.26017 Liflyand, E.; Tikhonov, S. 46 2011 Best approximation and moduli of smoothness: Computation and equivalence theorems. Zbl 1215.42002 Tikhonov, Sergey 46 2008 On generalized Lipschitz classes and Fourier series. Zbl 1065.26005 Tikhonov, Sergey 33 2004 Integral norm discretization and related problems. Zbl 07179262 Dai, F.; Prymak, A.; Temlyakov, V. N.; Tikhonov, S. Yu. 33 2019 Integrability and continuity of functions represented by trigonometric series: coefficients criteria. Zbl 1169.42001 Dyachenko, Mikhail; Tikhonov, Sergey 32 2009 Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates. Zbl 1252.42011 Gorbachev, Dmitry; Tikhonov, Sergey 30 2012 Positive \(L^p\)-bounded Dunkl-type generalized translation operator and its applications. Zbl 1416.42007 Gorbachev, D. V.; Ivanov, V. I.; Tikhonov, S. Yu. 29 2019 Smoothness conditions and Fourier series. Zbl 1124.26002 Tikhonov, Sergey 29 2007 Nikolskii inequality and Besov, Triebel-Lizorkin, Wiener and Beurling spaces on compact homogeneous manifolds. Zbl 1356.35022 Nursultanov, Erlan; Ruzhansky, Michael; Tikhonov, Sergey 27 2016 Net spaces and boundedness of integral operators. Zbl 1248.46025 Nursultanov, Erlan; Tikhonov, Sergey 27 2011 Analysis on \(h\)-harmonics and Dunkl transforms. Edited by Sergey Tikhonov. Zbl 1323.33003 Dai, Feng; Xu, Yuan 26 2015 Extended solution of Boas’ conjecture on Fourier transforms. Zbl 1151.42002 Liflyand, Elijah; Tikhonov, Sergey 26 2008 Sharp Jackson inequalities. Zbl 1136.41003 Dai, F.; Ditzian, Z.; Tikhonov, S. 25 2008 Trigonometric series of Nikol’skii classes. Zbl 1121.42006 Tikhonov, S. 25 2007 Embedding theorems in constructive approximation. Zbl 1172.46023 Simonov, B. V.; Tikhonov, S. Yu. 25 2008 Weighted Fourier inequalities: Boas’ conjecture in \({\mathbb{R}}^{n}\). Zbl 1246.42011 Gorbachev, D.; Liflyand, E.; Tikhonov, S. 25 2011 On sharp constants in Bernstein-Nikolskii inequalities. Zbl 1370.41023 Ganzburg, Michael I.; Tikhonov, Sergey Yu. 23 2017 The Fourier transforms of general monotone functions. Zbl 1297.42009 Liflyand, E.; Tikhonov, S. 23 2009 Mixed moduli of smoothness in \(L_{p}\): a survey. Zbl 1285.26008 Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu. 23 2013 Function spaces of logarithmic smoothness: embeddings and characterizations. Zbl 1512.46001 Domínguez, Óscar; Tikhonov, Sergey 23 2023 Sharp Ul’yanov-type inequalities using fractional smoothness. Zbl 1215.26011 Simonov, Boris; Tikhonov, Sergey 21 2010 Properties of moduli of smoothness in \(L_p (\mathbb{R}^d)\). Zbl 1450.41004 Kolomoitsev, Yurii; Tikhonov, Sergey 20 2020 Convergence of trigonometric series with general monotone coefficients. Zbl 1141.42004 Dyachenko, Mikhail; Tikhonov, Sergey 19 2007 A sharp Remez inequality for trigonometric polynomials. Zbl 1280.41011 Nursultanov, E.; Tikhonov, S. 19 2013 Convolution inequalities in Lorentz spaces. Zbl 1235.44012 Nursultanov, Erlan; Tikhonov, Sergey 18 2011 Sharp Pitt inequality and logarithmic uncertainty principle for Dunkl transform in \(L^2\). Zbl 1334.42020 Gorbachev, D. V.; Ivanov, V. I.; Tikhonov, S. Yu. 17 2016 Ulyanov-type inequalities between Lorentz-Zygmund spaces. Zbl 1316.41010 Gogatishvili, Amiran; Opic, Bohumír; Tikhonov, Sergey; Trebels, Walter 16 2014 Weak type inequalities for moduli of smoothness: The case of limit value parameters. Zbl 1217.41015 Tikhonov, Sergey 16 2010 Entropy numbers and Marcinkiewicz-type discretization. Zbl 1469.41013 Dai, F.; Prymak, A.; Shadrin, A.; Temlyakov, V.; Tikhonov, S. 16 2021 On the uniform convergence of trigonometric series. Zbl 1183.42005 Tikhonov, S. Yu. 15 2007 General monotone sequences and convergence of trigonometric series. Zbl 1167.42303 Dyachenko, M.; Tikhonov, S. 14 2008 Pitt and Boas inequalities for Fourier and Hankel transforms. Zbl 1307.44004 De Carli, L.; Gorbachev, D.; Tikhonov, S. 13 2013 Extending tests for convergence of number series. Zbl 1216.40001 Liflyand, E.; Tikhonov, S.; Zeltser, M. 13 2011 Weighted norm inequalities for integral transforms. Zbl 1410.42013 Gorbachev, Dmitry; Liflyand, Elijah; Tikhonov, Sergey 13 2018 Hardy-Littlewood and Ulyanov inequalities. Zbl 07403469 Kolomoitsev, Yurii; Tikhonov, Sergey 13 2021 Sparse approximation with bases. Based on advanced courses given at the Centre de Recerca Matemàtica, Barcelona, Spain, November 2011. Edited by Sergey Tikhonov. Zbl 1317.41019 Temlyakov, Vladimir 12 2015 Nikolskii constants for polynomials on the unit sphere. Zbl 1441.41003 Dai, Feng; Gorbachev, Dmitry; Tikhonov, Sergey 12 2020 A Hardy-Littlewood theorem for multiple series. Zbl 1283.42031 Dyachenko, Mikhail; Tikhonov, Sergey 12 2008 Uniform convergence and integrability of Fourier integrals. Zbl 1201.42003 Dyachenko, Mikhail; Liflyand, Elijah; Tikhonov, Sergey 12 2010 On the integrability of trigonometric series. Zbl 1136.42003 Tikhonov, S. Yu. 12 2005 Pitt inequalities and restriction theorems for the Fourier transform. Zbl 1381.42018 De Carli, Laura; Gorbachev, Dmitry; Tikhonov, Sergey 12 2017 Smoothness and asymptotic properties of functions with general monotone Fourier coefficients. Zbl 1412.42005 Dyachenko, M. I.; Tikhonov, S. Yu. 12 2018 On \(L_1\)-convergence of Fourier series. Zbl 1257.42009 Tikhonov, Sergey 12 2008 On embeddings of function classes defined by constructive characteristics. Zbl 1115.46029 Simonov, Boris V.; Tikhonov, Sergey Yu. 11 2006 Moduli of smoothness of functions and their derivatives. Zbl 1141.26005 Ditzian, Z.; Tikhonov, S. 11 2007 On moduli of smoothness of fractional order. Zbl 1108.26004 Tikhonov, S. 11 2005 Two-sided weighted Fourier inequalities. Zbl 1278.42006 Liflyand, Elijah; Tikhonov, Sergey 11 2012 Riesz potential and maximal function for Dunkl transform. Zbl 1480.42028 Gorbachev, D. V.; Ivanov, V. I.; Tikhonov, S. Yu. 11 2021 Sampling discretization of integral norms. Zbl 1480.65060 Dai, F.; Prymak, A.; Shadrin, A.; Temlyakov, V.; Tikhonov, S. 11 2021 Nikolskii inequality and functional classes on compact Lie groups. Zbl 1339.46038 Nursultanov, E. D.; Ruzhansky, M. V.; Tikhonov, S. Yu. 10 2015 Weighted norm inequalities for convolution and Riesz potential. Zbl 1307.31017 Nursultanov, Erlan; Tikhonov, Sergey 10 2015 Embeddings and characterizations of Lipschitz spaces. Zbl 1458.46023 Domínguez, Óscar; Haroske, Dorothee D.; Tikhonov, Sergey 10 2020 Relations between mixed moduli of smoothness, and embedding theorems for Nikol’skii classes. Zbl 1213.46032 Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu. 10 2010 Ulyanov-type inequalities and generalized Liouville derivatives. Zbl 1213.26010 Tikhonov, Sergey; Trebels, Walter 10 2011 Hardy-Littlewood theorems for trigonometric series with general monotone coefficients. Zbl 1436.42008 Dyachenko, Mikhail; Mukanov, Askhat; Tikhonov, Sergey 10 2020 Relations between moduli of smoothness in different metrics. Zbl 1304.41010 Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu. 9 2009 Uniform convergence of trigonometric series with general monotone coefficients. Zbl 1427.42003 Dyachenko, Mikhail; Mukanov, Askhat; Tikhonov, Sergey 9 2019 Constructive characteristics of mixed moduli of smoothness of positive orders. Zbl 1298.41020 Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu. 8 2012 Remez-type and Nikol’skii-type inequalities: general relations and the hyperbolic cross polynomials. Zbl 1381.41015 Temlyakov, V.; Tikhonov, S. 8 2017 Embedding results in questions of strong approximation by Fourier series. Zbl 1121.42005 Tikhonov, Sergey 8 2006 Weighted Paley-Wiener theorem on the Hilbert transform. (Version avec poids du théorème de Paley-Wiener sur la transformée de Hilbert.) Zbl 1210.42019 Liflyand, Elijah; Tikhonov, Sergey 8 2010 Strong approximation of Fourier series and embedding theorems. Zbl 1120.42002 Tikhonov, Sergey 7 2005 Hardy-Littlewood and Pitt’s inequalities for Hausdorff operators. Zbl 1409.42006 Dyachenko, M.; Nursultanov, E.; Tikhonov, S. 7 2018 Uncertainty principles for eventually constant sign bandlimited functions. Zbl 1450.42006 Gorbachev, Dmitry; Ivanov, Valerii; Tikhonov, Sergey 7 2020 Regularity of the Monge-Ampère equation in Besov’s spaces. Zbl 1290.35098 Kolesnikov, Alexander V.; Tikhonov, Sergey Yu. 7 2014 Wiener’s problem for positive definite functions. Zbl 1402.42011 Gorbachev, D. V.; Tikhonov, S. Yu. 7 2018 Two power-weight inequalities for the Hilbert transform on the cones of monotone functions. Zbl 1237.44005 Stepanov, Vladimir D.; Tikhonov, Sergey Yu. 7 2011 Smoothness of functions and Fourier coefficients. Zbl 1422.42006 D’yachenko, Mikhaĭl Ivanovich; Mukanov, Askhat Birlesovich; Tikhonov, Sergeĭ Yur’evich 7 2019 Two-weight inequalities for the Hilbert transform of monotone functions. Zbl 1253.26034 Stepanov, V. D.; Tikhonov, S. Yu. 7 2011 Characteristics of Besov-Nikol’skiĭ class of functions. Zbl 1114.42002 Tikhonov, Sergey 6 2005 Relations for moduli of smoothness in various metrics: functions with restrictions on the Fourier coefficients. Zbl 1204.42007 Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu. 6 2009 On the kernel of the \((\kappa, a)\)-generalized Fourier transform. Zbl 1528.42016 Gorbachev, Dmitry; Ivanov, Valerii; Tikhonov, Sergey 6 2023 Reverse Hölder’s inequality for spherical harmonics. Zbl 1366.33009 Dai, Feng; Feng, Han; Tikhonov, Sergey 5 2016 Functions with general monotone Fourier coefficients. Zbl 1496.42002 Belov, Aleksandr S.; Dyachenko, Mikhail I.; Tikhonov, Sergei Yu. 5 2021 Wiener’s positive Fourier coefficients theorem in variants of \(L^p\) spaces. Zbl 1204.42012 Ash, J. M.; Tikhonov, S.; Tung, J. 5 2010 Doubling condition at the origin for non-negative positive definite functions. Zbl 1412.42024 Gorbachev, Dmitry; Tikhonov, Sergey 5 2019 On the Besov and Besov-Nikol’skiĭ classes and on estimates for the mixed moduli of smoothness of fractional derivatives. Zbl 1089.46024 Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu. 5 2003 Weak monotonicity concept and its applications. Zbl 1334.40004 Tikhonov, S.; Zeltser, M. 4 2014 Weighted Fourier inequalities in Lebesgue and Lorentz spaces. Zbl 1439.42011 Nursultanov, Erlan; Tikhonov, Sergey 4 2020 Sharp Remez inequality. Zbl 1456.41002 Tikhonov, S.; Yuditskii, P. 4 2020 Norm inequalities for convolution operators. Zbl 1184.42005 Nursultanov, Erlan; Tikhonov, Sergey; Tleukhanova, Nazerke 4 2009 Wiener type theorems for Jacobi series with nonnegative coefficients. Zbl 1250.42084 Mhaskar, H. N.; Tikhonov, S. 4 2012 Hardy-type theorems on Fourier transforms revised. Zbl 1395.42003 Dyachenko, M.; Nursultanov, E.; Tikhonov, S. 3 2018 Weighted fractional Bernstein’s inequalities and their applications. Zbl 1350.26022 Dai, Feng; Tikhonov, Sergey 3 2016 Sharp approximation theorems and Fourier inequalities in the Dunkl setting. Zbl 1452.42006 Gorbachev, D. V.; Ivanov, V. I.; Tikhonov, S. Yu. 3 2020 An inequality of P. L. Ul’yanov. Zbl 1212.26029 Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu. 3 2008 Transformation of Fourier series using power and weakly oscillating sequences. Zbl 1094.42005 Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu. 3 2005 Wiener-Beurling spaces and their properties. Zbl 1440.46025 Nursultanov, Erlan; Tikhonov, Sergey 3 2020 Estimates of the asymptotic Nikolskii constants for spherical polynomials. Zbl 1470.33013 Dai, Feng; Gorbachev, Dmitry; Tikhonov, Sergey 3 2021 Jacobi weights, fractional integration, and sharp Ulyanov inequalities. Zbl 1321.41011 Glazyrina, Polina; Tikhonov, Sergey 2 2015 On two theorems of Lorentz. Zbl 1077.42004 Tikhonov, S. Yu. 2 2005 Norm convolution inequalities in Lebesgue spaces. Zbl 1404.44010 Erlan, Nursultanov; Tikhonov, Sergey; Tleukhanova, Nazerke 2 2018 Variable Lebesgue spaces and hyperbolic systems. Based on the presentations at two courses given under the title ‘Advanced courses on approximation theory and Fourier analysis’, Barcelona, Spain, November 7–11, 2011. Zbl 1297.46003 2 2014 Weighted gradient inequalities and unique continuation problems. Zbl 1439.42009 De Carli, Laura; Gorbachev, Dmitry; Tikhonov, Sergey 2 2020 Bernstein inequalities with nondoubling weights. Zbl 1362.26014 Bondarenko, Andrii; Tikhonov, Sergey 2 2017 Sparse grid approximation in weighted Wiener spaces. Zbl 1528.41036 Kolomoitsev, Yurii; Lomako, Tetiana; Tikhonov, Sergey 2 2023 Function spaces of logarithmic smoothness: embeddings and characterizations. Zbl 1512.46001 Domínguez, Óscar; Tikhonov, Sergey 23 2023 On the kernel of the \((\kappa, a)\)-generalized Fourier transform. Zbl 1528.42016 Gorbachev, Dmitry; Ivanov, Valerii; Tikhonov, Sergey 6 2023 Sparse grid approximation in weighted Wiener spaces. Zbl 1528.41036 Kolomoitsev, Yurii; Lomako, Tetiana; Tikhonov, Sergey 2 2023 On the cardinality of lower sets and universal discretization. Zbl 1515.65123 Dai, F.; Prymak, A.; Shadrin, A.; Temlyakov, V. N.; Tikhonov, S. 2 2023 New estimates for the maximal functions and applications. Zbl 1497.42043 Domínguez, Óscar; Tikhonov, Sergey 1 2022 Entropy numbers and Marcinkiewicz-type discretization. Zbl 1469.41013 Dai, F.; Prymak, A.; Shadrin, A.; Temlyakov, V.; Tikhonov, S. 16 2021 Hardy-Littlewood and Ulyanov inequalities. Zbl 07403469 Kolomoitsev, Yurii; Tikhonov, Sergey 13 2021 Riesz potential and maximal function for Dunkl transform. Zbl 1480.42028 Gorbachev, D. V.; Ivanov, V. I.; Tikhonov, S. Yu. 11 2021 Sampling discretization of integral norms. Zbl 1480.65060 Dai, F.; Prymak, A.; Shadrin, A.; Temlyakov, V.; Tikhonov, S. 11 2021 Functions with general monotone Fourier coefficients. Zbl 1496.42002 Belov, Aleksandr S.; Dyachenko, Mikhail I.; Tikhonov, Sergei Yu. 5 2021 Estimates of the asymptotic Nikolskii constants for spherical polynomials. Zbl 1470.33013 Dai, Feng; Gorbachev, Dmitry; Tikhonov, Sergey 3 2021 Weighted Fourier inequalities and boundedness of variation. Zbl 1462.42010 Tikhonov, Sergey Yu. 2 2021 Group actions: entropy, mixing, spectra, and generic properties. Zbl 1489.37003 Stepin, Anatoly; Tikhonov, Sergey 1 2021 Properties of moduli of smoothness in \(L_p (\mathbb{R}^d)\). Zbl 1450.41004 Kolomoitsev, Yurii; Tikhonov, Sergey 20 2020 Nikolskii constants for polynomials on the unit sphere. Zbl 1441.41003 Dai, Feng; Gorbachev, Dmitry; Tikhonov, Sergey 12 2020 Embeddings and characterizations of Lipschitz spaces. Zbl 1458.46023 Domínguez, Óscar; Haroske, Dorothee D.; Tikhonov, Sergey 10 2020 Hardy-Littlewood theorems for trigonometric series with general monotone coefficients. Zbl 1436.42008 Dyachenko, Mikhail; Mukanov, Askhat; Tikhonov, Sergey 10 2020 Uncertainty principles for eventually constant sign bandlimited functions. Zbl 1450.42006 Gorbachev, Dmitry; Ivanov, Valerii; Tikhonov, Sergey 7 2020 Weighted Fourier inequalities in Lebesgue and Lorentz spaces. Zbl 1439.42011 Nursultanov, Erlan; Tikhonov, Sergey 4 2020 Sharp Remez inequality. Zbl 1456.41002 Tikhonov, S.; Yuditskii, P. 4 2020 Sharp approximation theorems and Fourier inequalities in the Dunkl setting. Zbl 1452.42006 Gorbachev, D. V.; Ivanov, V. I.; Tikhonov, S. Yu. 3 2020 Wiener-Beurling spaces and their properties. Zbl 1440.46025 Nursultanov, Erlan; Tikhonov, Sergey 3 2020 Weighted gradient inequalities and unique continuation problems. Zbl 1439.42009 De Carli, Laura; Gorbachev, Dmitry; Tikhonov, Sergey 2 2020 Smoothness of functions versus smoothness of approximation processes. Zbl 1469.41015 Kolomoitsev, Yu. S.; Tikhonov, S. Yu. 2 2020 Nikolskii inequality for lacunary spherical polynomials. Zbl 1454.33012 Dai, Feng; Gorbachev, Dmitry; Tikhonov, Sergey 1 2020 Integral norm discretization and related problems. Zbl 07179262 Dai, F.; Prymak, A.; Temlyakov, V. N.; Tikhonov, S. Yu. 33 2019 Positive \(L^p\)-bounded Dunkl-type generalized translation operator and its applications. Zbl 1416.42007 Gorbachev, D. V.; Ivanov, V. I.; Tikhonov, S. Yu. 29 2019 Uniform convergence of trigonometric series with general monotone coefficients. Zbl 1427.42003 Dyachenko, Mikhail; Mukanov, Askhat; Tikhonov, Sergey 9 2019 Smoothness of functions and Fourier coefficients. Zbl 1422.42006 D’yachenko, Mikhaĭl Ivanovich; Mukanov, Askhat Birlesovich; Tikhonov, Sergeĭ Yur’evich 7 2019 Doubling condition at the origin for non-negative positive definite functions. Zbl 1412.42024 Gorbachev, Dmitry; Tikhonov, Sergey 5 2019 Hyperbolic cross approximation. Lecture notes given at the courses on constructive approximation and harmonic analysis, Barcelona, Spain, May 30 – June 3, 2016. Zbl 1414.41001 Dũng, Dinh; Temlyakov, Vladimir; Ullrich, Tino 97 2018 Weighted norm inequalities for integral transforms. Zbl 1410.42013 Gorbachev, Dmitry; Liflyand, Elijah; Tikhonov, Sergey 13 2018 Smoothness and asymptotic properties of functions with general monotone Fourier coefficients. Zbl 1412.42005 Dyachenko, M. I.; Tikhonov, S. Yu. 12 2018 Hardy-Littlewood and Pitt’s inequalities for Hausdorff operators. Zbl 1409.42006 Dyachenko, M.; Nursultanov, E.; Tikhonov, S. 7 2018 Wiener’s problem for positive definite functions. Zbl 1402.42011 Gorbachev, D. V.; Tikhonov, S. Yu. 7 2018 Hardy-type theorems on Fourier transforms revised. Zbl 1395.42003 Dyachenko, M.; Nursultanov, E.; Tikhonov, S. 3 2018 Norm convolution inequalities in Lebesgue spaces. Zbl 1404.44010 Erlan, Nursultanov; Tikhonov, Sergey; Tleukhanova, Nazerke 2 2018 On sharp constants in Bernstein-Nikolskii inequalities. Zbl 1370.41023 Ganzburg, Michael I.; Tikhonov, Sergey Yu. 23 2017 Pitt inequalities and restriction theorems for the Fourier transform. Zbl 1381.42018 De Carli, Laura; Gorbachev, Dmitry; Tikhonov, Sergey 12 2017 Remez-type and Nikol’skii-type inequalities: general relations and the hyperbolic cross polynomials. Zbl 1381.41015 Temlyakov, V.; Tikhonov, S. 8 2017 Bernstein inequalities with nondoubling weights. Zbl 1362.26014 Bondarenko, Andrii; Tikhonov, Sergey 2 2017 Pitt’s inequalities and uncertainty principle for generalized Fourier transform. Zbl 1404.42019 Gorbachev, Dmitry V.; Ivanov, Valerii I.; Tikhonov, Sergey Yu. 47 2016 Nikolskii inequality and Besov, Triebel-Lizorkin, Wiener and Beurling spaces on compact homogeneous manifolds. Zbl 1356.35022 Nursultanov, Erlan; Ruzhansky, Michael; Tikhonov, Sergey 27 2016 Sharp Pitt inequality and logarithmic uncertainty principle for Dunkl transform in \(L^2\). Zbl 1334.42020 Gorbachev, D. V.; Ivanov, V. I.; Tikhonov, S. Yu. 17 2016 Reverse Hölder’s inequality for spherical harmonics. Zbl 1366.33009 Dai, Feng; Feng, Han; Tikhonov, Sergey 5 2016 Weighted fractional Bernstein’s inequalities and their applications. Zbl 1350.26022 Dai, Feng; Tikhonov, Sergey 3 2016 Methods of Fourier analysis and approximation theory. Collected papers based on the presentations at the 9th ISAAC congress, section “Approximation theory and Fourier analysis”, Crakow, Poland, August 5–9, 2013 and at the conference on Fourier analysis and approximation theory in the CRM, Barcelona, Spain, November 4–8, 2013. Zbl 1343.42002 1 2016 Some problems in Fourier analysis and approximation theory. Zbl 1343.42001 Ruzhansky, Michael; Tikhonov, Sergey 1 2016 Analysis on \(h\)-harmonics and Dunkl transforms. Edited by Sergey Tikhonov. Zbl 1323.33003 Dai, Feng; Xu, Yuan 26 2015 Sparse approximation with bases. Based on advanced courses given at the Centre de Recerca Matemàtica, Barcelona, Spain, November 2011. Edited by Sergey Tikhonov. Zbl 1317.41019 Temlyakov, Vladimir 12 2015 Nikolskii inequality and functional classes on compact Lie groups. Zbl 1339.46038 Nursultanov, E. D.; Ruzhansky, M. V.; Tikhonov, S. Yu. 10 2015 Weighted norm inequalities for convolution and Riesz potential. Zbl 1307.31017 Nursultanov, Erlan; Tikhonov, Sergey 10 2015 Jacobi weights, fractional integration, and sharp Ulyanov inequalities. Zbl 1321.41011 Glazyrina, Polina; Tikhonov, Sergey 2 2015 Ulyanov-type inequalities between Lorentz-Zygmund spaces. Zbl 1316.41010 Gogatishvili, Amiran; Opic, Bohumír; Tikhonov, Sergey; Trebels, Walter 16 2014 Regularity of the Monge-Ampère equation in Besov’s spaces. Zbl 1290.35098 Kolesnikov, Alexander V.; Tikhonov, Sergey Yu. 7 2014 Weak monotonicity concept and its applications. Zbl 1334.40004 Tikhonov, S.; Zeltser, M. 4 2014 Variable Lebesgue spaces and hyperbolic systems. Based on the presentations at two courses given under the title ‘Advanced courses on approximation theory and Fourier analysis’, Barcelona, Spain, November 7–11, 2011. Zbl 1297.46003 2 2014 Mixed moduli of smoothness in \(L_{p}\): a survey. Zbl 1285.26008 Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu. 23 2013 A sharp Remez inequality for trigonometric polynomials. Zbl 1280.41011 Nursultanov, E.; Tikhonov, S. 19 2013 Pitt and Boas inequalities for Fourier and Hankel transforms. Zbl 1307.44004 De Carli, L.; Gorbachev, D.; Tikhonov, S. 13 2013 Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates. Zbl 1252.42011 Gorbachev, Dmitry; Tikhonov, Sergey 30 2012 Two-sided weighted Fourier inequalities. Zbl 1278.42006 Liflyand, Elijah; Tikhonov, Sergey 11 2012 Constructive characteristics of mixed moduli of smoothness of positive orders. Zbl 1298.41020 Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu. 8 2012 Wiener type theorems for Jacobi series with nonnegative coefficients. Zbl 1250.42084 Mhaskar, H. N.; Tikhonov, S. 4 2012 Trigonometric series with lacunary-monotone coefficients. Zbl 1266.42014 Dyachenko, M. I.; Tikhonov, S. 1 2012 A concept of general monotonicity and applications. Zbl 1223.26017 Liflyand, E.; Tikhonov, S. 46 2011 Net spaces and boundedness of integral operators. Zbl 1248.46025 Nursultanov, Erlan; Tikhonov, Sergey 27 2011 Weighted Fourier inequalities: Boas’ conjecture in \({\mathbb{R}}^{n}\). Zbl 1246.42011 Gorbachev, D.; Liflyand, E.; Tikhonov, S. 25 2011 Convolution inequalities in Lorentz spaces. Zbl 1235.44012 Nursultanov, Erlan; Tikhonov, Sergey 18 2011 Extending tests for convergence of number series. Zbl 1216.40001 Liflyand, E.; Tikhonov, S.; Zeltser, M. 13 2011 Ulyanov-type inequalities and generalized Liouville derivatives. Zbl 1213.26010 Tikhonov, Sergey; Trebels, Walter 10 2011 Two power-weight inequalities for the Hilbert transform on the cones of monotone functions. Zbl 1237.44005 Stepanov, Vladimir D.; Tikhonov, Sergey Yu. 7 2011 Two-weight inequalities for the Hilbert transform of monotone functions. Zbl 1253.26034 Stepanov, V. D.; Tikhonov, S. Yu. 7 2011 Sharp Ul’yanov-type inequalities using fractional smoothness. Zbl 1215.26011 Simonov, Boris; Tikhonov, Sergey 21 2010 Weak type inequalities for moduli of smoothness: The case of limit value parameters. Zbl 1217.41015 Tikhonov, Sergey 16 2010 Uniform convergence and integrability of Fourier integrals. Zbl 1201.42003 Dyachenko, Mikhail; Liflyand, Elijah; Tikhonov, Sergey 12 2010 Relations between mixed moduli of smoothness, and embedding theorems for Nikol’skii classes. Zbl 1213.46032 Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu. 10 2010 Weighted Paley-Wiener theorem on the Hilbert transform. (Version avec poids du théorème de Paley-Wiener sur la transformée de Hilbert.) Zbl 1210.42019 Liflyand, Elijah; Tikhonov, Sergey 8 2010 Wiener’s positive Fourier coefficients theorem in variants of \(L^p\) spaces. Zbl 1204.42012 Ash, J. M.; Tikhonov, S.; Tung, J. 5 2010 Integrability and continuity of functions represented by trigonometric series: coefficients criteria. Zbl 1169.42001 Dyachenko, Mikhail; Tikhonov, Sergey 32 2009 The Fourier transforms of general monotone functions. Zbl 1297.42009 Liflyand, E.; Tikhonov, S. 23 2009 Relations between moduli of smoothness in different metrics. Zbl 1304.41010 Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu. 9 2009 Relations for moduli of smoothness in various metrics: functions with restrictions on the Fourier coefficients. Zbl 1204.42007 Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu. 6 2009 Norm inequalities for convolution operators. Zbl 1184.42005 Nursultanov, Erlan; Tikhonov, Sergey; Tleukhanova, Nazerke 4 2009 Best approximation and moduli of smoothness: Computation and equivalence theorems. Zbl 1215.42002 Tikhonov, Sergey 46 2008 Extended solution of Boas’ conjecture on Fourier transforms. Zbl 1151.42002 Liflyand, Elijah; Tikhonov, Sergey 26 2008 Sharp Jackson inequalities. Zbl 1136.41003 Dai, F.; Ditzian, Z.; Tikhonov, S. 25 2008 Embedding theorems in constructive approximation. Zbl 1172.46023 Simonov, B. V.; Tikhonov, S. Yu. 25 2008 General monotone sequences and convergence of trigonometric series. Zbl 1167.42303 Dyachenko, M.; Tikhonov, S. 14 2008 A Hardy-Littlewood theorem for multiple series. Zbl 1283.42031 Dyachenko, Mikhail; Tikhonov, Sergey 12 2008 On \(L_1\)-convergence of Fourier series. Zbl 1257.42009 Tikhonov, Sergey 12 2008 An inequality of P. L. Ul’yanov. Zbl 1212.26029 Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu. 3 2008 Addendum to “Trigonometric series of Nikol’skii classes”. Zbl 1212.42011 Tikhonov, S. 1 2008 Trigonometric series with general monotone coefficients. Zbl 1106.42003 Tikhonov, S. 86 2007 Smoothness conditions and Fourier series. Zbl 1124.26002 Tikhonov, Sergey 29 2007 Trigonometric series of Nikol’skii classes. Zbl 1121.42006 Tikhonov, S. 25 2007 Convergence of trigonometric series with general monotone coefficients. Zbl 1141.42004 Dyachenko, Mikhail; Tikhonov, Sergey 19 2007 On the uniform convergence of trigonometric series. Zbl 1183.42005 Tikhonov, S. Yu. 15 2007 Moduli of smoothness of functions and their derivatives. Zbl 1141.26005 Ditzian, Z.; Tikhonov, S. 11 2007 On embeddings of function classes defined by constructive characteristics. Zbl 1115.46029 Simonov, Boris V.; Tikhonov, Sergey Yu. 11 2006 ...and 14 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 407 Authors 70 Tikhonov, Sergey Yur’evich 31 Volosivets, Sergeĭ Sergeevich 27 Gorbachëv, Dmitriĭ Viktorovich 24 Simonov, Boris Vital’evich 21 Mejjaoli, Hatem 21 Temlyakov, Vladimir Nikolaevich 20 Liflyand, Elijah 19 Nursultanov, Erlan D. 19 Potapov, Mikhaĭl Konstantinovich 18 Dai, Feng 18 Szal, Bogdan 17 D’yachenko, Mikhaĭl Ivanovich 16 Ruzhansky, Michael V. 14 Ivanov, Valerĭ Ivanovich 13 Daher, Radouan 12 Ganzburg, Michael Iosifovich 11 Kolomoitsev, Yurii S. 11 Prymak, Andriy V. 10 Dominguez, Oscar 8 Ben Saïd, Salem 8 Cardona, Duván 8 Ditzian, Zeev 7 Kofanov, V. A. 7 Leindler, László 7 Zhou, Songping 6 Negzaoui, Selma 6 Parui, Sanjay 6 Runovski, Konstantin Vsevolodovich 6 Stepanov, Vladimir Dmitrievich 6 Tleukhanova, Nazerke Tulekovna 6 Yao, Fengping 5 Akgun, Ramazan 5 Anoop, V. P. 5 Arestov, Vitaliĭ Vladimirovich 5 Debernardi, Alberto 5 Deikalova, Marina Valer’evna 5 Golubov, Boris Ivanovich 5 Kórus, Péter 5 Kosov, Egor D. 5 Kumar, Vishvesh 5 Trebels, Walter 5 Ullrich, Tino 4 Abdullayev, Fahreddin G. 4 Akylzhanov, Rauan Kh. 4 Bashirova, Anar Nabievna 4 Ghobber, Saifallah 4 Gogatishvili, Amiran 4 Jafarov, Sadulla Z. 4 Kalidolday, Aitolkyn Hunvaikyzy 4 Łenski, Włodzimierz 4 Limonova, Irina V. 4 Opic, Bohumír 4 Persson, Lars-Erik 4 Pesenson, Isaac Zalmanovich 4 Restrepo, Joel Esteban 4 Skopina, Mariya Aleksandrovna 4 Yu, Dansheng 3 Adcock, Ben 3 Aliev, Rashid Avazaga 3 Booton, Barry 3 Doktorski, Leo R. Ya. 3 Duong, Dao Van 3 Fei, Minggang 3 Gaál, Marcell 3 Haroske, Dorothee D. 3 Imron, Moch Aruman 3 Jordão, Thaís 3 Kokilashvili, Vakhtang 3 Kopezhanova, Aĭgerim Nurzhanovna 3 Krasniqi, Xhevat Z. 3 Kroó, András 3 Kubiak, Mateusz 3 Lomako, Tetiana 3 Loualid, El Mehdi 3 Martyanov, Ivan Anatol’evich 3 Mondal, Shyam Swarup 3 Nursultanov, Erlan Dautbekovich 3 Saadi, Faouaz 3 Shah, Firdous Ahmad 3 Shambilova, Guldarya Ermakovna 3 Suragan, Durvudkhan 3 Teng, Wentao 3 Tyr, Othman 3 Tyuleneva, Anna Anatol’evna 2 Amrahova, Aynur F. 2 Artamonov, Sergeĭ Yurievich 2 Berkak, El Mehdi 2 Boggarapu, Pradeep 2 Boubatra, Mohamed Amine 2 Burenkov, Viktor Ivanovich 2 Cardenas, Juan M. 2 Ciaurri, Óscar 2 Cobos, Fernando 2 Costarelli, Danilo 2 De Carli, Laura 2 de Nápoli, Pablo Luis 2 Debernardi Pinos, Alberto 2 Deleaval, Luc 2 Delgado, Julio 2 Draganov, Borislav R. ...and 307 more Authors all top 5 Cited in 166 Serials 42 Journal of Mathematical Analysis and Applications 29 Journal of Approximation Theory 28 Mathematical Notes 23 Analysis Mathematica 22 The Journal of Fourier Analysis and Applications 18 Acta Mathematica Hungarica 18 Proceedings of the Steklov Institute of Mathematics 18 Journal of Pseudo-Differential Operators and Applications 14 Ukrainian Mathematical Journal 14 Constructive Approximation 13 Journal of Mathematical Sciences (New York) 12 Moscow University Mathematics Bulletin 10 Integral Transforms and Special Functions 8 Complex Analysis and Operator Theory 7 Journal of Functional Analysis 7 Results in Mathematics 7 Mathematical Inequalities & Applications 7 Chebyshevskiĭ Sbornik 7 Eurasian Mathematical Journal 6 Proceedings of the American Mathematical Society 6 Journal of Complexity 6 Russian Mathematics 6 Journal of Inequalities and Applications 6 Comptes Rendus. 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Series II ...and 66 more Serials all top 5 Cited in 37 Fields 377 Harmonic analysis on Euclidean spaces (42-XX) 179 Approximations and expansions (41-XX) 148 Functional analysis (46-XX) 126 Real functions (26-XX) 67 Integral transforms, operational calculus (44-XX) 60 Operator theory (47-XX) 43 Special functions (33-XX) 38 Abstract harmonic analysis (43-XX) 31 Partial differential equations (35-XX) 25 Functions of a complex variable (30-XX) 25 Numerical analysis (65-XX) 23 Sequences, series, summability (40-XX) 17 Information and communication theory, circuits (94-XX) 14 Topological groups, Lie groups (22-XX) 8 Number theory (11-XX) 8 Probability theory and stochastic processes (60-XX) 8 Statistics (62-XX) 7 Difference and functional equations (39-XX) 7 Integral equations (45-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Potential theory (31-XX) 5 Computer science (68-XX) 4 Combinatorics (05-XX) 4 Dynamical systems and ergodic theory (37-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Fluid mechanics (76-XX) 1 \(K\)-theory (19-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Mechanics of particles and systems (70-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Citations by Year