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Uniform convergence of expansions into a multiple trigonometric Fourier series or a Fourier integral

I. L. Bloshanskii

M. V. Lomonosov Moscow State University

Abstract: Questions of convergence almost everywhere of expansions into a multiple trigonometric Fourier series or a Fourier integral are studied for functions from $L_p$, $p\ge1$, with summation over rectangles. Moreover, a ldquogeneralized localization principle,rdquo understood in the sense of convergence almost everywhere, is considered in the paper.

UDC: 517.51

Received: 10.09.1974

 English version: Mathematical Notes, 1975, 18:2, 675–684

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