Uniform convergence of Cesàro means of negative order of double trigonometric Fourier series

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2 Citations (Scopus)

Abstract

In this paper we prove that if f ∈ C([-π, π]2) and the function f is bounded partial p-variation for some p ∈ [1,+ ∞), then the double trigonometric Fourier series of a function f is uniformly (C;-α,-β) summable (α+β> 1/p, α, β> 0) in the sense of Pringsheim. If α + β ≥ 1/p, then there exists a continuous function f 0 of bounded partial p-variation on [-π, π]2 such that the Cesàro (C;-α,-β) means σ n,m -α,-β (f 0;0,0) of the double trigonometric Fourier series of f 0 diverge over cubes.

Original languageEnglish
Pages (from-to)255-265
Number of pages11
JournalAnalysis in Theory and Applications
Volume23
Issue number3
DOIs
Publication statusPublished - Sept 2007
Externally publishedYes

Keywords

  • Bounded variation
  • Cesàro means
  • Fourier series

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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