Convergence and localization in Orlicz classes for multiple Walsh-Fourier series with a lacunary sequence of rectangular partial sums

DOI10.1016/j.jmaa.2015.10.018zbMath1352.42012OpenAlexW2193533536MaRDI QIDQ892357

S. K. Bloshanskaya, Igor L. Bloshanskii

Publication date: 18 November 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2015.10.018

zbMATH Keywords

multiple Walsh-Fourier serieslacunary sequencerectangular partial sumsOrlicz classlocal smoothness conditionweak generalized localization

Mathematics Subject Classification ID

Fourier series and coefficients in several variables (42B05)

Cites Work

• Structural and geometric characteristics of sets of convergence and divergence of multiple Fourier series with \(J_k\)-lacunary sequence of rectangular partial sums
• A weak generalized localization criterion for multiple Walsh-Fourier series with \(J_k\)-lacunary sequence of rectangular partial sums
• A weak generalized localization criterion for multiple Fourier series whose rectangular partial sums are considered over a subsequence
• Trigonometric Fourier series and Walsh-Fourier series with lacunary sequence of partial sums
• Weak generalized localization for multiple Fourier series whose rectangular partial sums are considered with respect to some subsequence
• An inequality of Paley and convergence a.e. of Walsh-Fourier series
• On the convergence of lacunary Walsh-Fourier series
• Generalized localization for the multiple Walsh-Fourier series of functions in $ L_p$, $ p\geqslant 1$
• Sur la convergence presque partout des séries de Fourier-Walsh des fonctions de l'espace L²(0,1)
• WEYL MULTIPLIERS FOR MULTIPLE FOURIER SERIES
• STRUCTURAL AND GEOMETRIC CHARACTERISTICS OF SETS OF CONVERGENCE AND DIVERGENCE OF MULTIPLE FOURIER SERIES OF FUNCTIONS WHICH EQUAL ZERO ON SOME SET
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