Integrability of double trigonometric series with special coefficients
type: Item
instance of: scholarly article
title: Integrability of double trigonometric series with special coefficients
zbMATH Open document ID: 0784.42011
DOI: 10.1007/BF01906772
published in: Analysis Mathematica
publication date: 1992-06-25T00:00:00Z
review text: Double cosine- and sine-series are considered and also series with respect to mixed harmonics, the coefficients of which tend to zero and constitute a sequence of bounded variation. Along with rectangular partial sums of such series modified sums are investigated, and necessary and sufficient conditions for their regular convergence in the metric of \(L^ 1=L^ 1\bigl( [0,\pi] \times [0,\pi] \bigr)\) are established. As corollaries, coefficient conditions for the integrability of the sum of a double trigonometric series are established; under the same conditions it is the Fourier series of its sum, and the rectangular partial sums converge regularly in the metric of \(L^ 1\). We note that for one- dimensional cosine-series similar modified sums were introduced and considered by \textit{J. W. Garrett} and \textit{Č. V. Stanojević} [Proc. Am. Math. Soc. 60, 68-71 (1976; Zbl 0339.42007)], and analogous results for them were established by these authors; one-dimensional sine-series were considered by the author in Stud. Math. 92, No. 2, 187-200 (1989; Zbl 0571.42006).
Mathematics Subject Classification ID: 42B05
zbMATH DE Number: 5973
zbMATH Keywords: double cosine series
zbMATH Keywords: double sine series
zbMATH Keywords: double trigonometric series
zbMATH Keywords: Fourier series
author: Ferenc Móricz
MaRDI profile type: Publication
cites work: Q4084167
cites work: On the convergence in a restricted sense of multiple series
cites work: Über Fourier-Koeffizienten
cites work: Stone Duality for Nominal Boolean Algebras with И
cites work: The Brauer-Manin Obstruction and III[2]
cites work: Q3254471
full work available at URL: https://doi.org/10.1007/bf01906772
OpenAlex ID: W2313891394
description: scientific article; zbMATH DE number 5973