Variable Hardy and Hardy-Lorentz spaces and applications in Fourier analysis

Research output: Contribution to journalArticle

Abstract

We summarize some results about the variable Hardy and Hardy- Lorentz spaces Hp(·)(ℝd) and Hp(·),q(ℝd) and about the θ-summability of multidimensional Fourier transforms. We prove that the maximal operator of the - means is bounded from Hp(·)(ℝd) to Lp(·)(ℝd) and from Hp(·);q(ℝd) to Lp(·);q(ℝd). This implies some norm and almost everywhere convergence results for the Riesz, Bochner-Riesz, Weierstrass, Picard and Bessel summations.

Original languageEnglish
Pages (from-to)381-393
Number of pages13
JournalStudia Universitatis Babes-Bolyai Mathematica
Volume63
Issue number3
DOIs
Publication statusPublished - Jan 1 2018

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Keywords

  • Atomic decomposition
  • Maximal operator
  • Variable Hardy spaces
  • Variable Hardy-Lorentz spaces
  • θ-summability

ASJC Scopus subject areas

  • Mathematics(all)

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