Abstract:
We obtain structural and geometric characteristics of sets on which weak generalized localization almost everywhere is valid for multiple trigonometric Fourier series of functions in the classes $L(\log^+L)^{3k+2}(\mathbb T^N)$, $1\le k\le N-2$, $N\ge 3$, in the case where the rectangular partial sums of these series have a “number” in which exactly $k$ components are terms of lacunary sequences.
Keywords:trigonometric Fourier series, lacunary sequence of partial sums, localization for Fourier series, Orlicz class of functions, Lebesgue measure.
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