Maximal functions along surfaces on product domains

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Abstract

In this paper, we study the L p boundedness for a class of maximal functions along surfaces in ℝn × ℝm of the form {(φ1(|u|)u′, φ2(|v|)v′) : (u,v) ∈ ℝn × ℝm}.We prove that such maximal functions are bounded on L p for all 2 ≤ p < ∞ provided that the functions φ1 and φ2 satisfy certain oscillatory estimates of van der Corput type.

Original languageEnglish
Pages (from-to)163-175
Number of pages13
JournalAnalysis Mathematica
Volume34
Issue number3
DOIs
Publication statusPublished - Sep 2008

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ASJC Scopus subject areas

  • Mathematics(all)

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