Multiple trigonometric series with lexicographically monotone coefficients
type: Item
instance of: scholarly article
title: Multiple trigonometric series with lexicographically monotone coefficients
zbMATH Open document ID: 0716.42014
DOI: 10.1007/BF01906082
author: M. I. Dyachenko
published in: Analysis Mathematica
publication date: 1990-01-01T00:00:00Z
review text: The author considers series of the type described in the title on the n- dimensional torus. He imposes an additional hypothesis on the growth of the coefficients, which he shows is always satisfied for a trigonometric series that is the Fourier series of an \(L_ p\)-function, \(1<p<\infty.\) Under these conditions he shows that the series is Pringsheim-convergent almost everywhere for \(p>n,\) but with \(p=n\) there exists an \(L_ p\)- function whose Fourier series has lexicographically monotone coefficients and diverges almost everywhere when arranged cubically.
Mathematics Subject Classification ID: 42B05
zbMATH DE Number: 4180038
zbMATH Keywords: multiple trigonometric series
zbMATH Keywords: Fourier series
zbMATH Keywords: Pringsheim-convergent
zbMATH Keywords: lexicographically monotone coefficients
reviewed by: Roger L. Cooke
MaRDI profile type: Publication
cites work: Q3506242
cites work: Convergence almost everywhere of certain singular integrals and multiple Fourier series
cites work: On trigonometric series conjugate to Fourier series of two variables
cites work: Period, index and potential \(\text Ш\)
full work available at URL: https://doi.org/10.1007/bf01906082
OpenAlex ID: W1945634123
description: scientific article; zbMATH DE number 4180038