Restricted summability of Fourier transforms and local Hardy spaces

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A general summability method, the so-called Θ-summability is considered for multi-dimensional Fourier transforms. Under some conditions on Θ, it is proved that the maximal operator of the Θ-means defined in a cone is bounded from the amalgam Hardy space W(hp, ℓ) to W(Lp, ℓ). This implies the almost everywhere convergence of the Θ-means in a cone for all f ∈ W(L1, ℓ) ⊃ L1.

Original languageEnglish
Pages (from-to)1627-1640
Number of pages14
JournalActa Mathematica Sinica, English Series
Volume26
Issue number9
DOIs
Publication statusPublished - 2010

Fingerprint

Summability
Hardy Space
Cones
Fourier transform
Fourier transforms
Cone
Amalgam
Mercury amalgams
Almost Everywhere Convergence
Maximal Operator
Mathematical operators
Imply

Keywords

  • Θ-summability of Fourier transforms
  • atomic decomposition
  • local Hardy spaces
  • Wiener amalgam spaces

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Restricted summability of Fourier transforms and local Hardy spaces. / Weisz, F.

In: Acta Mathematica Sinica, English Series, Vol. 26, No. 9, 2010, p. 1627-1640.

Research output: Contribution to journalArticle

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