Cesàro summability of two-parameter trigonometric-Fourier series

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6 Citations (Scopus)

Abstract

The two-dimensional classical Hardy spaces Hp(T×T) on the bidisc are introduced and it is shown that the maximal operator of the Cesàro means of a distribution is bounded from Hp(T×T) to Lp(T2) (3/4<p≤∞) and is of weak type (H#1(T×T), L1(T2)) where the Hardy space H#1(T×T) is defined by the hybrid maximal function. As a consequence we obtain that the Cesàro means of a function f∈H#1(T×T) ⊃L log L(T2) converge a.e. to the function in question.

Original languageEnglish
Pages (from-to)30-45
Number of pages16
JournalJournal of Approximation Theory
Volume90
Issue number1
DOIs
Publication statusPublished - Jul 1997

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Mathematics(all)
  • Applied Mathematics

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