Boundedness of cesàro and Riesz means in variable dyadic hardy spaces

Kristóf Szarvas, Ferenc Weisz

Research output: Contribution to journalArticle

Abstract

We consider two types of maximal operators. We prove that, under some conditions, each maximal operator is bounded from the classical dyadic martingale Hardy space Hp to the classical Lebesgue space Lp and from the variable dyadic martingale Hardy space Hp(·) to the variable Lebesgue space Lp(·). Using this, we can prove the boundedness of the Cesàro and Riesz maximal operator from Hp(·) to Lp(·) and from the variable Hardy-Lorentz space Hp(·),q to the variable Lorentz space Lp(·),q. As a consequence, we can prove theorems about almost everywhere and norm convergence.

Original languageEnglish
Pages (from-to)675-696
Number of pages22
JournalBanach Journal of Mathematical Analysis
Volume13
Issue number3
DOIs
Publication statusPublished - Jan 1 2019

    Fingerprint

Keywords

  • Boundedness
  • Cesàro and Riesz maximal operator
  • Cesàro means
  • Riesz means
  • Variable Hardy spaces
  • Variable Hardy-Lorentz spaces

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

Cite this