Stepanov, V. D.; Ushakova, E. P. Boundedness and compactness of the two-dimensional rectangular Hardy operator. (English. Russian original) Zbl 1518.47080 Dokl. Math. 106, No. 2, 361-365 (2022); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 506, 68-72 (2022). MSC: 47G10 47B92 46E30 PDFBibTeX XMLCite \textit{V. D. Stepanov} and \textit{E. P. Ushakova}, Dokl. Math. 106, No. 2, 361--365 (2022; Zbl 1518.47080); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 506, 68--72 (2022) Full Text: DOI
Stepanov, V. D.; Shambilova, G. E. Bilinear weighted inequalities with two-dimensional operators. (English. Russian original) Zbl 1481.26018 Dokl. Math. 102, No. 2, 406-408 (2020); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 494, 60-63 (2020). MSC: 26D10 46E30 PDFBibTeX XMLCite \textit{V. D. Stepanov} and \textit{G. E. Shambilova}, Dokl. Math. 102, No. 2, 406--408 (2020; Zbl 1481.26018); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 494, 60--63 (2020) Full Text: DOI
Jain, P.; Stepanov, V. D.; Shambilova, G. E. Discrete bilinear Hardy inequalities. (English. Russian original) Zbl 1444.26031 Dokl. Math. 100, No. 3, 554-557 (2019); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 489, No. 5, 445-448 (2019). Reviewer: Sanja Varošanec (Zagreb) MSC: 26D15 PDFBibTeX XMLCite \textit{P. Jain} et al., Dokl. Math. 100, No. 3, 554--557 (2019; Zbl 1444.26031); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 489, No. 5, 445--448 (2019) Full Text: DOI
Stepanov, V. D.; Shambilova, G. E. Multidimensional bilinear Hardy inequalities. (English. Russian original) Zbl 1440.26024 Dokl. Math. 100, No. 1, 374-376 (2019); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 487, No. 5, 496-498 (2019). Reviewer: Sanja Varošanec (Zagreb) MSC: 26D15 46E30 PDFBibTeX XMLCite \textit{V. D. Stepanov} and \textit{G. E. Shambilova}, Dokl. Math. 100, No. 1, 374--376 (2019; Zbl 1440.26024); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 487, No. 5, 496--498 (2019) Full Text: DOI
Stepanov, V. D.; Shambilova, G. E. Bilinear weighted inequalities with Volterra integral operators. (English. Russian original) Zbl 07125253 Dokl. Math. 99, No. 3, 290-294 (2019); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 486, No. 4, 416-420 (2019). MSC: 47-XX PDFBibTeX XMLCite \textit{V. D. Stepanov} and \textit{G. E. Shambilova}, Dokl. Math. 99, No. 3, 290--294 (2019; Zbl 07125253); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 486, No. 4, 416--420 (2019) Full Text: DOI
Jain, P.; Kanjilal, S.; Stepanov, V. D.; Ushakova, E. P. On bilinear Hardy-Steklov operators. (English. Russian original) Zbl 1480.47067 Dokl. Math. 98, No. 3, 634-637 (2018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 483, No. 6, 596-599 (2018). Reviewer: Vladimir S. Pilidi (Rostov-na-Donu) MSC: 47G10 47A07 PDFBibTeX XMLCite \textit{P. Jain} et al., Dokl. Math. 98, No. 3, 634--637 (2018; Zbl 1480.47067); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 483, No. 6, 596--599 (2018) Full Text: DOI
Prokhorov, D. V.; Stepanov, V. D.; Ushakova, E. P. Spaces associated with weighted Sobolev spaces on the real line. (English. Russian original) Zbl 1409.46028 Dokl. Math. 98, No. 1, 373-376 (2018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 481, No. 5, 486-489 (2018). MSC: 46E35 PDFBibTeX XMLCite \textit{D. V. Prokhorov} et al., Dokl. Math. 98, No. 1, 373--376 (2018; Zbl 1409.46028); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 481, No. 5, 486--489 (2018) Full Text: DOI
Stepanov, V. D.; Ushakova, E. P. Hardy-Steklov operators and duality principle in weighted Sobolev spaces of the first order. (English. Russian original) Zbl 1403.47004 Dokl. Math. 97, No. 3, 232-235 (2018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 480, No. 2, 150-154 (2018). Reviewer: Dmitri V. Prokhorov (Saratov) MSC: 47G10 46A20 46E35 PDFBibTeX XMLCite \textit{V. D. Stepanov} and \textit{E. P. Ushakova}, Dokl. Math. 97, No. 3, 232--235 (2018; Zbl 1403.47004); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 480, No. 2, 150--154 (2018) Full Text: DOI
Jain, P.; Singh, A. P.; Singh, M.; Stepanov, V. D. Sawyer duality principle in grand Lebesgue spaces. (English. Russian original) Zbl 06892214 Dokl. Math. 97, No. 1, 18-19 (2018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 478, No. 2, 131-132 (2018). MSC: 47-XX 42-XX PDFBibTeX XMLCite \textit{P. Jain} et al., Dokl. Math. 97, No. 1, 18--19 (2018; Zbl 06892214); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 478, No. 2, 131--132 (2018) Full Text: DOI
Stepanov, V. D.; Shambilova, G. E. On bilinear weighted inequalities on the cone of nondecreasing functions. (English. Russian original) Zbl 1390.26046 Dokl. Math. 96, No. 3, 631-635 (2017); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 477, No. 6, 652-656 (2017). Reviewer: James Adedayo Oguntuase (Abeokuta) MSC: 26D15 26D10 PDFBibTeX XMLCite \textit{V. D. Stepanov} and \textit{G. E. Shambilova}, Dokl. Math. 96, No. 3, 631--635 (2017; Zbl 1390.26046); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 477, No. 6, 652--656 (2017) Full Text: DOI
Stepanov, V. D.; Shambilova, G. E. Boundedness of quasilinear integral operators of iterated type with Oinarov’s kernel on the cone of monotone functions. (English. Russian original) Zbl 1495.45009 Dokl. Math. 96, No. 1, 315-320 (2017); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 475, No. 1, 17-23 (2016). MSC: 45P05 PDFBibTeX XMLCite \textit{V. D. Stepanov} and \textit{G. E. Shambilova}, Dokl. Math. 96, No. 1, 315--320 (2017; Zbl 1495.45009); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 475, No. 1, 17--23 (2016) Full Text: DOI
Stepanov, V. D.; Shambilova, G. E. Boundedness of a class of quasilinear operators on the cone of monotone functions. (English. Russian original) Zbl 1489.47071 Dokl. Math. 94, No. 3, 697-702 (2016); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 471, No. 6, 645-650 (2016). MSC: 47G10 PDFBibTeX XMLCite \textit{V. D. Stepanov} and \textit{G. E. Shambilova}, Dokl. Math. 94, No. 3, 697--702 (2016; Zbl 1489.47071); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 471, No. 6, 645--650 (2016) Full Text: DOI
Prokhorov, D. V.; Stepanov, V. D.; Ushakova, E. P. On weighted Sobolev spaces on the real line. (English. Russian original) Zbl 1358.46032 Dokl. Math. 93, No. 1, 78-81 (2016); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 466, No. 5, 522-525 (2016). MSC: 46E35 46E30 PDFBibTeX XMLCite \textit{D. V. Prokhorov} et al., Dokl. Math. 93, No. 1, 78--81 (2016; Zbl 1358.46032); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 466, No. 5, 522--525 (2016) Full Text: DOI
Stepanov, V. D. On optimal Banach spaces containing a weighted cone of monotone or quasi-concave functions. (English. Russian original) Zbl 1344.46025 Dokl. Math. 92, No. 2, 545-547 (2015); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 464, No. 2, 145-147 (2015). MSC: 46E30 PDFBibTeX XMLCite \textit{V. D. Stepanov}, Dokl. Math. 92, No. 2, 545--547 (2015; Zbl 1344.46025); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 464, No. 2, 145--147 (2015) Full Text: DOI
Stepanov, V. D.; Shambilova, G. E. Weight boundedness of a class of quasilinear operators on the cone of monotone functions. (English. Russian original) Zbl 1311.47013 Dokl. Math. 90, No. 2, 569-572 (2014); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 458, No. 3, 268-271 (2014). Reviewer: V. Lokesha (Bangalore) MSC: 47A30 26D10 PDFBibTeX XMLCite \textit{V. D. Stepanov} and \textit{G. E. Shambilova}, Dokl. Math. 90, No. 2, 569--572 (2014; Zbl 1311.47013); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 458, No. 3, 268--271 (2014) Full Text: DOI
Prokhorov, D. V.; Stepanov, V. D. Estimates for a class of sublinear integral operators. (English. Russian original) Zbl 1303.45008 Dokl. Math. 89, No. 3, 372-377 (2014); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 456, No. 6, 645-649 (2014). MSC: 45P05 PDFBibTeX XMLCite \textit{D. V. Prokhorov} and \textit{V. D. Stepanov}, Dokl. Math. 89, No. 3, 372--377 (2014; Zbl 1303.45008); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 456, No. 6, 645--649 (2014) Full Text: DOI
Prokhorov, D. V.; Stepanov, V. D. Weighted estimates for a class of sublinear operators. (English. Russian original) Zbl 1310.47066 Dokl. Math. 88, No. 3, 721-723 (2013); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 453, No. 5, 486-488 (2013). Reviewer: Harun Karsli (Bolu) MSC: 47G10 26D10 26D15 PDFBibTeX XMLCite \textit{D. V. Prokhorov} and \textit{V. D. Stepanov}, Dokl. Math. 88, No. 3, 721--723 (2013; Zbl 1310.47066); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 453, No. 5, 486--488 (2013) Full Text: DOI
Gogatishvili, A.; Persson, L.-E.; Stepanov, V. D.; Wall, P. On scales of equivalent conditions characterizing weighted Stieltjes inequality. (English. Russian summary) Zbl 1261.42005 Dokl. Math. 86, No. 3, 738-739 (2012); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 447, No. 1, 13-14 (2012). MSC: 42A38 PDFBibTeX XMLCite \textit{A. Gogatishvili} et al., Dokl. Math. 86, No. 3, 738--739 (2012; Zbl 1261.42005); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 447, No. 1, 13--14 (2012) Full Text: DOI
Gogatishvili, A.; Stepanov, V. D. Integral operators on cones of monotone functions. (English. Russian original) Zbl 1263.47057 Dokl. Math. 86, No. 2, 650-653 (2012); translation from Dokl. Akad. Nauk. 446, No. 4, 367-370 (2012). Reviewer: Fayou Zhao (Shanghai) MSC: 47G10 26D10 26D15 26D07 PDFBibTeX XMLCite \textit{A. Gogatishvili} and \textit{V. D. Stepanov}, Dokl. Math. 86, No. 2, 650--653 (2012; Zbl 1263.47057); translation from Dokl. Akad. Nauk. 446, No. 4, 367--370 (2012) Full Text: DOI
Gogatishvili, A.; Stepanov, V. D. Integral operators on cones of monotone functions. (English. Russian original) Zbl 1281.26014 Dokl. Math. 86, No. 1, 562-565 (2012); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 445, No. 6, 618-621 (2012). Reviewer: Joaquím Martín (Barcelona) MSC: 26D10 PDFBibTeX XMLCite \textit{A. Gogatishvili} and \textit{V. D. Stepanov}, Dokl. Math. 86, No. 1, 562--565 (2012; Zbl 1281.26014); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 445, No. 6, 618--621 (2012) Full Text: DOI
Prokhorov, D. V.; Stepanov, V. D. On supremum operators. (English. Russian original) Zbl 1236.47008 Dokl. Math. 84, No. 1, 457-458 (2011); translation from Dokl. Akad. Nauk 439, No. 1, 28-29 (2011). Reviewer: Florian-Horia Vasilescu (Villeneuve d’Ascq) MSC: 47A30 47G10 46E30 PDFBibTeX XMLCite \textit{D. V. Prokhorov} and \textit{V. D. Stepanov}, Dokl. Math. 84, No. 1, 457--458 (2011; Zbl 1236.47008); translation from Dokl. Akad. Nauk 439, No. 1, 28--29 (2011) Full Text: DOI
Stepanov, V. D.; Tikhonov, S. Yu. Two-weight inequalities for the Hilbert transform of monotone functions. (English. Russian original) Zbl 1253.26034 Dokl. Math. 83, No. 2, 241-242 (2011); translation from Dokl. Akad. Nauk 437, No. 5, 606-608 (2011). Reviewer: James Adedayo Oguntuase (Abeokuta) MSC: 26D10 26A33 PDFBibTeX XMLCite \textit{V. D. Stepanov} and \textit{S. Yu. Tikhonov}, Dokl. Math. 83, No. 2, 241--242 (2011; Zbl 1253.26034); translation from Dokl. Akad. Nauk 437, No. 5, 606--608 (2011) Full Text: DOI
Stepanov, V. D.; Persson, L. E.; Popova, O. V. Two-sided Hardy-type inequalities for monotone functions. (English. Russian original) Zbl 1196.26033 Dokl. Math. 80, No. 3, 814-817 (2009); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 429, No. 2, 159-162 (2009). Reviewer: B. G. Pachpatte (Aurangabad) MSC: 26D15 PDFBibTeX XMLCite \textit{V. D. Stepanov} et al., Dokl. Math. 80, No. 3, 814--817 (2009; Zbl 1196.26033); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 429, No. 2, 159--162 (2009) Full Text: DOI
Stepanov, V. D.; Ushakova, E. P. Weight estimates for norms of operators with two variable limits of integration. (English. Russian original) Zbl 1230.47061 Dokl. Math. 78, No. 1, 541-543 (2008); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 421, No. 3, 318-320 (2008). Reviewer: George O. Okikiolu (London) MSC: 47B38 42B35 46E30 47G10 PDFBibTeX XMLCite \textit{V. D. Stepanov} and \textit{E. P. Ushakova}, Dokl. Math. 78, No. 1, 541--543 (2008; Zbl 1230.47061); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 421, No. 3, 318--320 (2008) Full Text: DOI
Lomakina, E. N.; Stepanov, V. D. Asymptotic estimates for approximative and entropy numbers of the one-weight Riemann-Liouville operator. (English. Russian original) Zbl 1127.47304 Dokl. Math. 72, No. 1, 574-575 (2005); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 403, No. 5, 598-599 (2005). Reviewer: Aleksandar Perović (Berlin) MSC: 47B06 44A35 PDFBibTeX XMLCite \textit{E. N. Lomakina} and \textit{V. D. Stepanov}, Dokl. Math. 72, No. 1, 574--575 (2005; Zbl 1127.47304); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 403, No. 5, 598--599 (2005)
Stepanov, V. D. An extremal property of classical orthogonal polynomials. (English. Russian original) Zbl 1274.42064 Dokl. Math. 72, No. 1, 555-557 (2005); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 403, No. 4, 452-454 (2005). MSC: 42C05 41A10 PDFBibTeX XMLCite \textit{V. D. Stepanov}, Dokl. Math. 72, No. 1, 555--557 (2005; Zbl 1274.42064); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 403, No. 4, 452--454 (2005)
Persson, L. E.; Stepanov, V. D.; Ushakova, E. P. On integral operators with monotone kernels. (English. Russian original) Zbl 1152.45309 Dokl. Math. 72, No. 1, 491-494 (2005); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 403, No. 1, 11-14 (2005). MSC: 45P05 47G10 26D15 44A10 44A15 PDFBibTeX XMLCite \textit{L. E. Persson} et al., Dokl. Math. 72, No. 1, 491--494 (2005; Zbl 1152.45309); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 403, No. 1, 11--14 (2005)
Stepanov, V. D.; Khludnev, A. M. The fictitious domain method as applied to the Signorini problem. (English. Russian original) Zbl 1161.35028 Dokl. Math. 68, No. 2, 161-166 (2003); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 392, No. 1, 17-20 (2003). Reviewer: Messoud A. Efendiev (Berlin) MSC: 35J65 74G15 PDFBibTeX XMLCite \textit{V. D. Stepanov} and \textit{A. M. Khludnev}, Dokl. Math. 68, No. 2, 161--166 (2003; Zbl 1161.35028); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 392, No. 1, 17--20 (2003)
Prokhorov, D. V.; Stepanov, V. D. On Riemann-Liouville operators. (English. Russian original) Zbl 1146.47305 Dokl. Math. 65, No. 1, 64-76 (2002); translation from Dokl. Akad. Nauk 382, No. 4, 452-455 (2002). MSC: 47G10 PDFBibTeX XMLCite \textit{D. V. Prokhorov} and \textit{V. D. Stepanov}, Dokl. Math. 65, No. 1, 64--76 (2002; Zbl 1146.47305); translation from Dokl. Akad. Nauk 382, No. 4, 452--455 (2002)
Persson, L.-E.; Stepanov, V. D. Weighted integral inequalities with a geometric mean. (English. Russian original) Zbl 1044.26014 Dokl. Math. 63, No. 2, 201-202 (2001); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 377, No. 4, 439-440 (2001). Reviewer: Bohumír Opic (Praha) MSC: 26D15 26E60 26D10 PDFBibTeX XMLCite \textit{L. E. Persson} and \textit{V. D. Stepanov}, Dokl. Math. 63, No. 2, 439--440 (2001; Zbl 1044.26014); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 377, No. 4, 439--440 (2001)
Lomakina, E. N.; Stepanov, V. D. The asymptotic behavior of approximation numbers and estimates of the Schatten-von Neumann norms for the Hardy integral operator. (English. Russian original) Zbl 0990.47044 Dokl. Math. 60, No. 1, 94-96 (1999); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 367, No. 5, 594-596 (1999). Reviewer: H.Tanabe (Toyonaka) MSC: 47G10 47B06 47B10 47B38 PDFBibTeX XMLCite \textit{E. N. Lomakina} and \textit{V. D. Stepanov}, Dokl. Math. 60, No. 1, 594--596 (1999; Zbl 0990.47044); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 367, No. 5, 594--596 (1999)
Lomakina, E. N.; Stepanov, V. D. Operators of the Hardy-type in Banach function spaces on the semiaxis. (English. Russian original) Zbl 0958.47022 Dokl. Math. 57, No. 2, 187-189 (1998); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 359, No. 1, 21-23 (1998). MSC: 47G10 47B06 45P05 47B07 46E30 PDFBibTeX XMLCite \textit{E. N. Lomakina} and \textit{V. D. Stepanov}, Dokl. Math. 57, No. 2, 21--23 (1998; Zbl 0958.47022); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 359, No. 1, 21--23 (1998)
Gol’dman, M. L.; Stepanov, V. D.; Heinig, H. P. On the principle of duality in Lorentz spaces. (English. Russian original) Zbl 0889.46031 Dokl. Math. 52, No. 2, 264-267 (1995); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 344, No. 6, 740-744 (1995). Reviewer: R.Johnson (College Park) MSC: 46E30 46B10 42B20 42B25 PDFBibTeX XMLCite \textit{M. L. Gol'dman} et al., Dokl. Math. 52, No. 2, 264--267 (1995; Zbl 0889.46031); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 344, No. 6, 740--744 (1995)