Maximal functions along twisted surfaces on product domains

Ahmad Al-Salman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we introduce a class of maximal functions along twisted surfaces in Rn ×Rm of the form {(φ(|v|)u, ϕ(|u|)v): (u, v) ∈ Rn ×Rm }. We prove Lp bounds when the kernels lie in the space Lq (Sn−1 ×Sm−1). As a consequence, we establish the Lp boundedness for such class of operators provided that the kernels are in L log L(Sn−1 ×Sm−1) or in the Block spaces Bq0,0 (Sn−1 ×Sm−1) (q > 1).

Original languageEnglish
Pages (from-to)1003-1019
Number of pages17
JournalBulletin of the Korean Mathematical Society
Volume58
Issue number4
DOIs
Publication statusPublished - 2021
Externally publishedYes

Keywords

  • Block spaces
  • Maximal functions
  • Product domains
  • Singular integrals
  • Twisted surfaces

ASJC Scopus subject areas

  • Mathematics(all)

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