Singular integral operators with kernels supported in higher dimensional subvarieties

Ahmad Al-Salman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we introduce a class of singular Radon transforms on Rn with kernels supported in a subvariety in Rn× Rn determined by a polynomial mapping from Rn× Rn into Rn. The class of considered operators is related to the composition of homogeneous singular integral operators. We prove that the operators are bounded on Lp provided that the kernels are rough in L(log L) 2(Sn-1× Sn-1). The condition L(log L) 2(Sn-1× Sn-1) is observed to be optimal in the sense that the power 2 can not be replaced by a smaller number.

Original languageEnglish
Article number48
JournalBanach Journal of Mathematical Analysis
Volume16
Issue number3
DOIs
Publication statusPublished - Jul 2022

Keywords

  • Fourier transform
  • L estimates
  • Maximal functions
  • Rough kernels
  • Singular integral operators
  • Singular Radon transforms

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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