Weierstrass and Picard summability of more-dimensional Fourier transforms

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Abstract

It is proved that the maximal operator of the Weierstrass and Picard summability means of a tempered distribution is bounded from Hp (Rd ) to Lp (Rd ) for all and, consequently, is of weak type (1,1). As a consequence we obtain that the summability means of a function f (Rd) converge a.e. to f. Similar results are shown for conjugate functions and for Fourier series.

Original languageEnglish
Pages (from-to)271-280
Number of pages10
JournalAnalysis (Germany)
Volume32
Issue number4
DOIs
Publication statusPublished - Jan 1 2012

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Keywords

  • Fourier transforms
  • Hardy spaces
  • Weierstrass and Picard summation

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

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