Maximal functions along surfaces on product domains

Ahmad Al-Salman

doi:10.1007/s10476-008-0301-8

Maximal functions along surfaces on product domains

Ahmad Al-Salman^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

In this paper, we study the L ^p boundedness for a class of maximal functions along surfaces in ℝⁿ × ℝ^m of the form {(φ₁(|u|)u′, φ₂(|v|)v′) : (u,v) ∈ ℝ_n × ℝ_m}.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 language	English
Pages (from-to)	163-175
Number of pages	13
Journal	Analysis Mathematica
Volume	34
Issue number	3
DOIs	https://doi.org/10.1007/s10476-008-0301-8
Publication status	Published - Sep 2008
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s10476-008-0301-8

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AB - 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.

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JO - Analysis Mathematica

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ER -

Maximal functions along surfaces on product domains

Abstract

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