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Pointwise convergence of singular convolution integrals. (English) Zbl 0178.15302


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[1] G. Alexits , Konvergenzprobleme der Orthogonalreihen . Berlin , 1960 , MR 162091 | Zbl 0097.27702 · Zbl 0097.27702
[2] A. Benedek - A.P. Calderón - R. Panzone , Convolution operators on Banach space valued functions . Proc. Amer. Math. Soc. 48 ( 1962 ), 356 - 365 . MR 133653 | Zbl 0103.33402 · Zbl 0103.33402
[3] A.P. Calderón - A. Zygmund , On the existence of certain singular integrals . Acta Math. 88 ( 1952 ), 85 - 139 . MR 52553 | Zbl 0047.10201 · Zbl 0047.10201
[4] A.P. Calderón - A. Zygmund , On singular integrals . Amer. J. Math. 78 ( 1956 ), 289 - 309 . MR 84633 | Zbl 0072.11501 · Zbl 0072.11501
[5] M. Cotlar , Condiciones de continuidad de operadores potentiales y de Hilbert . Cursos y seminarios de matemática, Fasciculo 2 , Universidade de Buenos Aires , 1959 . MR 116190 | Zbl 0094.10101 · Zbl 0094.10101
[6] M. Cotlar , A unified theory of Hilbert transforms and ergodic theorems . Revista Mat. Cuyana 1 ( 1955 ), 105 - 167 . MR 84632 | Zbl 0071.33402 · Zbl 0071.33402
[7] L. Hörmander , Estimates for translation invariant operaters in Lp spaces . Acta. Math. 104 ( 1960 ), 93 - 140 . MR 121655 | Zbl 0093.11402 · Zbl 0093.11402
[8] W. Littman , Multipliers in Lp and interpolation . Bull. Amer. Math. Soc. 77 ( 1965 ), 764 - 766 . Article | MR 179544 | Zbl 0156.36504 · Zbl 0156.36504
[9] L. Loomis , A note on the Hilbert transform . Bull. Amer. Math. Soc. 52 ( 1946 ), 1082 - 1086 . Article | MR 19155 | Zbl 0063.03630 · Zbl 0063.03630
[10] S.G. Michlin , On the multipliers of Fourier integrals . Dokl. Akad. Nauk. SSSR 109 ( 1956 ), 701 - 703 . (Russian.) MR 80799 | Zbl 0073.08402 · Zbl 0073.08402
[11] S.G. Michlin , Fourier integrals and multiple singular integrals . Vestnik Leningrad. Univ. Ser. Mat. Mech. Astr. 12 ( 1957 ), 143 - 155 . (Russian) MR 88603 | Zbl 0092.31701 · Zbl 0092.31701
[12] R. O’ Neil - G. Weiss , The Hilbert transform, and rearrangement of functions . Studia Math. 23 ( 1963 ), 189 - 198 . Article | MR 160084 | Zbl 0118.09901 · Zbl 0118.09901
[13] J. Peetre , Espaces d’interpolation, généralisations, applications , Rend. Sem. Mat. Fis. Milano 34 ( 1964 ), 133 - 164 . MR 172107 | Zbl 0151.17902 · Zbl 0151.17902
[14] J. Peetre , Applications de la théorie des espaces d’interpolation dans l’analyse harmonique . To appear. in Riceeche Mat. Zbl 0154.15302 · Zbl 0154.15302
[15] J. Peetre , Espaces d’interpolation et théorème de Soboleff . To appear in Ann. Inst. Fourien. Numdam | Zbl 0151.17903 · Zbl 0151.17903
[16] J. Sckw Artz , A remark on inequalities of Calderòn - Zygmund type for vector-valued functions . Comm. Pure Appl. Math. 14 ( 1961 ), 785 - 799 . MR 143031 | Zbl 0106.08104 · Zbl 0106.08104
[17] E.M. Stein . G. Weiss , An extension of a theorem of Marcinkiewicz and some of its applications . J. Math. Mech. 8 ( 1959 ), 263 - 284 . MR 107163 | Zbl 0084.10801 · Zbl 0084.10801
[18] G. Weiss , Analisis armonico en varias variables. Teoria de los espacios Hp Cursos y seminarios de matemátua , Fasciculo 9 , Universidade de Buenos Aires , 1960 . MR 139902 | Zbl 0100.10501 · Zbl 0100.10501
[19] A. Zygmund , Trigonometrical series . Cambridge , 1959 . · Zbl 0085.05601
[20] A. Zygmund , On singular integrals . Rend. Mat. 16 ( 1957 ), 468 - 505 . MR 96088 | Zbl 0088.08302 · Zbl 0088.08302
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