A class of parabolic maximal functions

Ghada Shakkah, Ahmad Al-Salman

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper, we prove Lp estimates of a class of parabolic maximal functions provided that their kernels are in Lq . Using the obtained estimates, we prove the boundedness of the maximal functions under very weak conditions on the kernel. In particular, we prove the Lp -boundedness of our maximal functions when their kernels are in Llog L1/2 (Sn-1 ) or in the block space Bq 0,?1/2(Sn?1 ), q>1.

Original languageEnglish
Pages (from-to)1-31
Number of pages31
JournalCommunications in Mathematical Analysis
Volume19
Issue number2
Publication statusPublished - 2016

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Keywords

  • Block space.
  • Maximal functions
  • Oscillatory integrals
  • Parabolic maximal functions
  • Singular integrals

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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