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- W2193533536 abstract "For functions f in Orlicz classes, we consider multiple Walsh–Fourier series for which the rectangular partial sums Sn(x;f) have indices n=(n1,…,nN)∈ZN (N≥3), where either N or N−1 components are elements of (single) lacunary sequences. For this series, we prove the validity of weak generalized localization almost everywhere on an arbitrary measurable set A⊂IN={x∈RN:0≤xj<1,j=1,2,…,N}, in the case when the structure and geometry of A are defined by the properties Bk, 2≤k≤N. We define the relation between the parameter k and the “smoothness” of functions in terms of the Orlicz classes. As a consequence, we obtain some results on the “local smoothness conditions.” In particular, the theorem is proved for the convergence of Walsh–Fourier series on an arbitrary open set Ω⊂IN under the minimal conditions imposed on the smoothness of the function on this set." @default.
- W2193533536 created "2016-06-24" @default.
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- W2193533536 date "2016-03-01" @default.
- W2193533536 modified "2023-09-24" @default.
- W2193533536 title "Convergence and localization in Orlicz classes for multiple Walsh–Fourier series with a lacunary sequence of rectangular partial sums" @default.
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- W2193533536 doi "https://doi.org/10.1016/j.jmaa.2015.10.018" @default.
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