Variable anisotropic hardy spaces and their applications

Jun Liu, F. Weisz, Dachun Yang, Wen Yuan

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Let p(·): ℝn → (0, ∞] be a variable exponent function satisfying the globally log-Hölder continuous condition and A a general expansive matrix on ℝn. In this article, the authors first introduce the variable anisotropic Hardy space HA p(·)(ℝn) associated with A, via the non-tangential grand maximal function, and then establish its radial or non-tangential maximal function characterizations. Moreover, the authors also obtain various equivalent characterizations of HA p(·)(ℝn), respectively, by means of atoms, finite atoms, the Lusin area function, the Littlewood-Paley g-function or gλ -function. As applications, the authors first establish a criterion on the boundedness of sublinear operators from HA p(·)(ℝn) into a quasi-Banach space. Then, applying this criterion, the authors show that the maximal operators of the Bochner-Riesz and the Weierstrass means are bounded from HA p(·)(ℝn) to Lp(·)(ℝn) and, as consequences, some almost everywhere and norm convergences of these Bochner-Riesz and Weierstrass means are also obtained. These results on the Bochner-Riesz and the Weierstrass means are new even in the isotropic case.

Original languageEnglish
Pages (from-to)1173-1216
Number of pages44
JournalTaiwanese Journal of Mathematics
Volume22
Issue number5
DOIs
Publication statusPublished - Oct 1 2018

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Keywords

  • (finite) atom
  • (variable) Hardy space
  • And phrases
  • Bochner-Riesz means
  • Expansive matrix
  • Grand maximal function
  • Littlewood-Paley function
  • Weierstrass means

ASJC Scopus subject areas

  • Mathematics(all)

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