Local Hardy spaces and summability of Fourier transforms

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

New Wiener amalgam spaces are introduced for local Hardy spaces. 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 is bounded from the amalgam space W (hp, ℓ) to W (Lp, ℓ). This implies the almost everywhere convergence of the θ-means for all f ∈ W (L1, ℓ) ⊃ L1.

Original languageEnglish
Pages (from-to)275-285
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume362
Issue number2
DOIs
Publication statusPublished - Feb 15 2010

Fingerprint

Mercury amalgams
Summability
Hardy Space
Fourier transform
Fourier transforms
Wiener Amalgam Spaces
Amalgam
Almost Everywhere Convergence
Maximal Operator
Imply

Keywords

  • θ-summability of Fourier transforms
  • Atomic decomposition
  • Local Hardy spaces
  • Wiener amalgam spaces

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

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

In: Journal of Mathematical Analysis and Applications, Vol. 362, No. 2, 15.02.2010, p. 275-285.

Research output: Contribution to journalArticle

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