Norm convergence of double Fourier series on unbounded Vilenkin groups

G. Gát; U. Goginava

doi:10.1007/s10474-017-0703-9

Norm convergence of double Fourier series on unbounded Vilenkin groups

G. Gát
, U. Goginava

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We study approximation by rectangular partial sums of double Fourier series on unbounded Vilenkin groups in the spaces C and L₁. From these results we obtain criterions of the uniform convergence and L-convergence of double Vilenkin–Fourier series. We also prove that these results are sharp.

Original language	English
Pages (from-to)	201-216
Number of pages	16
Journal	Acta Mathematica Hungarica
Volume	152
Issue number	1
DOIs	https://doi.org/10.1007/s10474-017-0703-9
Publication status	Published - Jun 1 2017
Externally published	Yes

Keywords

convergence in norm
modulus of continuity
unbounded Vilenkin system

ASJC Scopus subject areas

General Mathematics

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10.1007/s10474-017-0703-9

Cite this

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title = "Norm convergence of double Fourier series on unbounded Vilenkin groups",

abstract = "We study approximation by rectangular partial sums of double Fourier series on unbounded Vilenkin groups in the spaces C and L1. From these results we obtain criterions of the uniform convergence and L-convergence of double Vilenkin–Fourier series. We also prove that these results are sharp.",

keywords = "convergence in norm, modulus of continuity, unbounded Vilenkin system",

author = "G. G{\'a}t and U. Goginava",

note = "Publisher Copyright: {\textcopyright} 2017, Akad{\'e}miai Kiad{\'o}, Budapest, Hungary.",

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T1 - Norm convergence of double Fourier series on unbounded Vilenkin groups

AU - Gát, G.

AU - Goginava, U.

PY - 2017/6/1

Y1 - 2017/6/1

N2 - We study approximation by rectangular partial sums of double Fourier series on unbounded Vilenkin groups in the spaces C and L1. From these results we obtain criterions of the uniform convergence and L-convergence of double Vilenkin–Fourier series. We also prove that these results are sharp.

AB - We study approximation by rectangular partial sums of double Fourier series on unbounded Vilenkin groups in the spaces C and L1. From these results we obtain criterions of the uniform convergence and L-convergence of double Vilenkin–Fourier series. We also prove that these results are sharp.

KW - convergence in norm

KW - modulus of continuity

KW - unbounded Vilenkin system

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UR - https://www.scopus.com/pages/publications/85015652081#tab=citedBy

U2 - 10.1007/s10474-017-0703-9

DO - 10.1007/s10474-017-0703-9

M3 - Article

AN - SCOPUS:85015652081

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JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

IS - 1

ER -

Norm convergence of double Fourier series on unbounded Vilenkin groups

Abstract

Keywords

ASJC Scopus subject areas

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