1-Summability of d-Dimensional Fourier Transforms

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

A general summability method of more-dimensional Fourier transforms is given with the help of a continuous function θ. Under some weak conditions on θ we show that the maximal operator of the ℓ1-θ-means of a tempered distribution is bounded from Hp(d) to Lp(d) for all d/(d+α)

1-θ-means of a function f∈L1(d) converge a. e. to f. Moreover, we prove that the ℓ1-θ-means are uniformly bounded on the spaces Hp(d), and so they converge in norm (d/(d+α)1-θ-summation are considered, such as the Weierstrass, Picar, Bessel, Fejér, de La Vallée-Poussin, Rogosinski, and Riesz summations.

Original languageEnglish
Pages (from-to)421-452
Number of pages32
JournalConstructive Approximation
Volume34
Issue number3
DOIs
Publication statusPublished - Dec 2011

Fingerprint

Summability
Fourier transform
Fourier transforms
Summation
Converge
Tempered Distribution
Maximal Operator
Friedrich Wilhelm Bessel
Continuous Function
Norm

Keywords

  • ℓ-θ-summation
  • Fourier transforms
  • Hardy spaces
  • Interpolation
  • p-atom

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis
  • Computational Mathematics

Cite this

1-Summability of d-Dimensional Fourier Transforms. / Weisz, F.

In: Constructive Approximation, Vol. 34, No. 3, 12.2011, p. 421-452.

Research output: Contribution to journalArticle

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