The Hardy-Littlewood theorem for double Fourier-Haar series from mixed metric Lebesgue Lp[0,1]2 and net Np, q(M) spaces

被引：0

作者：

Bashirova, A. N. ^{[1
]}

Nursultanov, E. D. ^{[2
]}

机构：

[1] LN Gumilyov Eurasian Natl Univ, 13 Kazhymukan Munaitpasov St,Z01C0X0, Nur Sultan, Kazakhstan

[2] Moscow MV Lomonosov State Univ, Kazakhstan Branch, 11 Kazhymukan Munaitpasov St,Z01C0T6, Nur Sultan, Kazakhstan

来源：

ANALYSIS MATHEMATICA | 2022年 / 48卷 / 01期

关键词：

net space; Lebesgue space; anisotropic space; Fourier series; Haar system; PALEY INEQUALITIES; INTERPOLATION; MULTIPLIERS;

D O I：

10.1007/s10476-022-0115-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain a criterion given in terms of the Fourier-Haar co-efficients for the function f(x(1), x(2)) to belong to the net space N-p,N- q(M) and to the Lebesgue space L-p[0, 1](2) with mixed metric, where 1 < p < infinity,0 < q <= infinity, p =(p(1), p(2)), q=(q(1), q(2)) and M is the set of all rectangles in Double-struck capital R-2. We prove the Hardy-Littlewood theorem for multiple Fourier-Haar series.

引用

页码：5 / 17

页数：13

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