Riesz means associated with certain product type convex domain

Sunggeum Hong, Joonil Kim, Chan Woo Yang

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this paper we study the maximal operators Tδ* and the convolution operators Tδ associated with multipliers of the form. We prove that Tδ* satisfies the sharp weak type (p,p) inequality on Hp(Rn) when 2(n-1)2n-1<p<1 and δ=n(1p-1)+12, or when p=2(n-1)2n-1 and δ>n(1p-1)+12. We also obtain that Tδ is bounded from Lp(Rn) to Lp(Rn) for δ>max{2|1p-12|-12,0} and 1<;p<∞. The indicated ranges of parameters p and δ cannot be improved.

Original languageEnglish
Pages (from-to)585-606
Number of pages22
JournalJournal of Mathematical Analysis and Applications
Volume380
Issue number2
DOIs
Publication statusPublished - 2011 Aug 15

Keywords

  • Certain product type
  • Convex domain
  • Lp bound
  • Multipliers
  • Weak type (p,p)

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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