L p estimates of rough maximal functions along surfaces with applications

Ahmad Al-Salman, Abdulla M. Jarrah

Research output: Contribution to journalArticle

Abstract

In this paper, we study the Lp mapping properties of certain class of maximal oscillatory singular integral operators. We prove a general theorem for a class of maximal functions along surfaces. As a consequence of such theorem, we establish the Lp boundedness of various maximal oscillatory singular integrals provided that their kernels belong to the natural space Llog L(Sn−1). Moreover, we highlight some additional results concerning operators with kernels in certain block spaces. The results in this paper substantially improve previously known results.

Original languageEnglish
Pages (from-to)925-942
Number of pages18
JournalActa Mathematica Sinica, English Series
Volume32
Issue number8
DOIs
Publication statusPublished - Aug 1 2016

Keywords

  • highly monotone curves
  • maximal functions
  • Oscillatory singular integrals
  • rough kernels

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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