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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2014, Volume 285, Pages 41–63
DOI: https://doi.org/10.1134/S0371968514020058
(Mi tm3547)
 

This article is cited in 1 scientific paper (total in 1 paper)

A weak generalized localization criterion for multiple Walsh–Fourier series with $J_k$-lacunary sequence of rectangular partial sums

S. K. Bloshanskayaa, I. L. Bloshanskiib

a National Engineering Physics Institute "MEPhI", Moscow, Russia
b Moscow State Region University, Moscow, Russia
Full-text PDF (335 kB) Citations (1)
References:
Abstract: We obtain a criterion for the validity of weak generalized localization almost everywhere on an arbitrary set of positive measure $\mathfrak A$, $\mathfrak A\subset\mathbb I^N=\{x\in\mathbb R^N\colon0\leq x_j<1,\, j=1,2,\dots,N\}$, $N\geq3$ (in terms of the structure and geometry of the set $\mathfrak A$), for multiple Walsh–Fourier series (summed over rectangles) of functions $f$ in the classes $L_p(\mathbb I^N)$, $p>1$ (i.e., necessary and sufficient conditions for the convergence almost everywhere of the Fourier series on some subset of positive measure $\mathfrak A_1$ of the set $\mathfrak A$, when the function expanded in a series equals zero on $\mathfrak A$), in the case when the rectangular partial sums $S_n(x;f)$ of this series have indices $n=(n_1,\dots,n_N)\in\mathbb Z^N$ in which some components are elements of (single) lacunary sequences.
Received in September 2013
English version:
Proceedings of the Steklov Institute of Mathematics, 2014, Volume 285, Pages 34–55
DOI: https://doi.org/10.1134/S0081543814040051
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: S. K. Bloshanskaya, I. L. Bloshanskii, “A weak generalized localization criterion for multiple Walsh–Fourier series with $J_k$-lacunary sequence of rectangular partial sums”, Selected topics of mathematical physics and analysis, Collected papers. In commemoration of the 90th anniversary of Academician Vasilii Sergeevich Vladimirov's birth, Trudy Mat. Inst. Steklova, 285, MAIK Nauka/Interperiodica, Moscow, 2014, 41–63; Proc. Steklov Inst. Math., 285 (2014), 34–55
Citation in format AMSBIB
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\by S.~K.~Bloshanskaya, I.~L.~Bloshanskii
\paper A weak generalized localization criterion for multiple Walsh--Fourier series with $J_k$-lacunary sequence of rectangular partial sums
\inbook Selected topics of mathematical physics and analysis
\bookinfo Collected papers. In commemoration of the 90th anniversary of Academician Vasilii Sergeevich Vladimirov's birth
\serial Trudy Mat. Inst. Steklova
\yr 2014
\vol 285
\pages 41--63
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\crossref{https://doi.org/10.1134/S0371968514020058}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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