Marcinkiewicz-summability of multi-dimensional Fourier transforms and Fourier series

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

A generalization of Marcinkiewicz-summability of multi-dimensional Fourier transforms and Fourier series is investigated with the help of a continuous function θ Under some weak conditions on θ we show that the maximal operator of the Marcinkiewicz-θ-means of a tempered distribution is bounded from Hp(Xd) to Lp(Xd) for all d/(d+α)

p(Xd) and so they converge in norm (d/(d+α)

Original languageEnglish
Pages (from-to)910-929
Number of pages20
JournalJournal of Mathematical Analysis and Applications
Volume379
Issue number2
DOIs
Publication statusPublished - Jul 15 2011

Fingerprint

Tempered Distribution
Maximal Operator
Fourier series
Summability
Fourier transform
Fourier transforms
Continuous Function
Converge
Norm
Generalization

Keywords

  • Fourier series
  • Fourier transforms
  • Hardy spaces
  • Interpolation
  • Marcinkiewicz--summation
  • P-Atom

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Marcinkiewicz-summability of multi-dimensional Fourier transforms and Fourier series. / Weisz, F.

In: Journal of Mathematical Analysis and Applications, Vol. 379, No. 2, 15.07.2011, p. 910-929.

Research output: Contribution to journalArticle

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