Analogs of the Luzin-Danzhu and Cantor-Lebesgue theorems for double trigonometric series

V. S. Panferov

doi:10.1007/bf01153564

Analogs of the Luzin-Danzhu and Cantor-Lebesgue theorems for double trigonometric series

Mathematical Notes ◽

10.1007/bf01153564 ◽

1975 ◽

Vol 18 (5) ◽

pp. 983-992

Author(s):

V. S. Panferov

Keyword(s):

Trigonometric Series ◽

Double Trigonometric Series

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Liouville–Weyl Derivatives of Double Trigonometric Series

Topics in Classical and Modern Analysis - Applied and Numerical Harmonic Analysis ◽

10.1007/978-3-030-12277-5_11 ◽

2019 ◽

pp. 159-182

Author(s):

Ainur Jumabayeva ◽

Boris Simonov

Keyword(s):

Trigonometric Series ◽

Double Trigonometric Series ◽

Derivatives Of

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Weighted integrability of double trigonometric series and of double series with respect to multiplicative systems with coefficients of class R 0 + BV S 2

Mathematical Notes ◽

10.1134/s0001434612030327 ◽

2012 ◽

Vol 91 (3-4) ◽

pp. 575-578 ◽

Cited By ~ 1

Author(s):

N. A. Bokayev ◽

Zh. B. Mukanov

Keyword(s):

Trigonometric Series ◽

Double Series ◽

Double Trigonometric Series ◽

Multiplicative Systems ◽

Weighted Integrability

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Uniform convergence of double trigonometric series

Mathematica Bohemica ◽

10.21136/mb.2013.143434 ◽

2013 ◽

Vol 138 (3) ◽

pp. 225-243

Author(s):

Péter Kórus

Keyword(s):

Uniform Convergence ◽

Trigonometric Series ◽

Double Trigonometric Series

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Sets of absolute convergence of double trigonometric series

Mathematical Notes ◽

10.1007/bf01158639 ◽

1972 ◽

Vol 11 (5) ◽

pp. 289-293

Author(s):

R. A. Avetisyan

Keyword(s):

Trigonometric Series ◽

Absolute Convergence ◽

Double Trigonometric Series

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Errata: Square Summation and Localization of Double Trigonometric Series

American Journal of Mathematics ◽

10.2307/2372555 ◽

1953 ◽

Vol 75 (4) ◽

pp. 872 ◽

Cited By ~ 1

Author(s):

V. L. Shapiro

Keyword(s):

Trigonometric Series ◽

Double Trigonometric Series

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Integrability of double trigonometric series with special coefficients

Analysis Mathematica ◽

10.1007/bf01906772 ◽

1990 ◽

Vol 16 (1) ◽

pp. 39-56 ◽

Cited By ~ 1

Author(s):

Ferenc Móricz

Keyword(s):

Trigonometric Series ◽

Double Trigonometric Series

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Weighted integrability of double trigonometric series

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-99-04661-4 ◽

1999 ◽

Vol 127 (5) ◽

pp. 1463-1471

Author(s):

Chang-Pao Chen ◽

Xin-Rong Huang

Keyword(s):

Trigonometric Series ◽

Double Trigonometric Series ◽

Weighted Integrability

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Square Summation and Localization of Double Trigonometric Series

American Journal of Mathematics ◽

10.2307/2372457 ◽

1953 ◽

Vol 75 (2) ◽

pp. 347 ◽

Cited By ~ 2

Author(s):

Victor L. Shapiro

Keyword(s):

Trigonometric Series ◽

Double Trigonometric Series

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Using double trigonometric series to compute ribbed cylindrical shells

Soviet Applied Mechanics ◽

10.1007/bf00887753 ◽

1966 ◽

Vol 2 (6) ◽

pp. 30-34 ◽

Cited By ~ 5

Author(s):

V. A. Zarutskii

Keyword(s):

Trigonometric Series ◽

Cylindrical Shells ◽

Double Trigonometric Series ◽

Ribbed Cylindrical Shells

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Norm inequalities in multidimensional Lorentz spaces

MATHEMATICA SCANDINAVICA ◽

10.7146/math.scand.a-15080 ◽

2008 ◽

Vol 103 (2) ◽

pp. 278

Author(s):

Boris Simonov ◽

Sergey Tikhonov

Keyword(s):

Trigonometric Series ◽

Sufficient Conditions ◽

Lorentz Spaces ◽

Necessary And Sufficient Conditions ◽

Double Trigonometric Series ◽

Norm Inequalities ◽

Necessary And Sufficient

In this paper we obtain necessary and sufficient conditions for double trigonometric series to belong to generalized Lorentz spaces, not symmetric in general. Estimates for the norms are given in terms of coefficients.

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