The question of A*-summability of double trigonometric Fourier series

descriptionPublicationkeyboard_double_arrow_right Article 01 Feb 1972 English Publisher:Springer Science and Business Media LLCJournal:Mathematical Notes of the Academy of Sciences of the USSR, volume 11, pages 93-96 (issn: 0001-4346, eissn: 1573-8876,

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Authors: Gogoladze, L. D.;

doi: 10.1007/bf01097923

The question of A*-summability of double trigonometric Fourier series

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Abstract

It is proved that for anyf(x, y) ∈ L(R), where R=[-π,π,-π, π], a function ϕ(x, y), exists such that ¦ϕ(x, y) ¦=¦f(x, y) ¦ for almost all (x, y) ∈ R. The Fourier series of the function ϕ(x, y) and all conjugate trigonometric series are A*-summable almost everywhere.

Related Organizations

Tbilisi State University
Georgia

Keywords

Fourier series and coefficients in several variables, Summability and absolute summability of Fourier and trigonometric series, Summability in several variables

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