The segal algebra ℝd and norm summability of fourier series and fourier transforms

Hans G. Feichtinger, Ferenc Weisz

Research output: Contribution to journalArticle

50 Citations (Scopus)

Abstract

A general summability method, the so-called θ-summability is considered for multi-dimensional Fourier series. Equivalent conditions are derived for the uniform and L 1-norm convergence of the θ-means σ n θ f to the function f. If f is in a homogeneous Banach space, then the preceeding convergence holds in the norm of the space. In case θ is an element of Feichtinger's Segal algebra S 0(ℝd)then these convergence results hold. Some new sufficient conditions are given for θ to be in S0(ℝ d). A long list of concrete special cases of the θ-summation is listed. The same results are also provided in the context of Fourier transforms, indicating how proofs have to be changed in this case.

Original languageEnglish
Pages (from-to)333-349
Number of pages17
JournalMonatshefte fur Mathematik
Volume148
Issue number4
DOIs
Publication statusPublished - Aug 1 2006

Keywords

  • Amalgam spaces
  • Besov-
  • Feichtinger's algebra
  • Fractional Sobolev spaces
  • Homogeneous Banach space
  • Sobolev-
  • Wiener algebra
  • θ-summability of Fourier series

ASJC Scopus subject areas

  • Mathematics(all)

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