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Singular and Marcinkiewicz integral operators on product domains

Badriya Al-Azri|Ahmad Al-Salman
대한수학회 (The Korean Mathematical Society)|2023.04|대한수학회논문집 (Communications of the KMS)|제38권 제2호|pp. 401-430|DOI 10.4134/CKMS.c210421

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키워드

convexSingular integral operators on product domains$L^{p}$ estimatesmaximal functionsHardy Littlewood maximal function
주제분류수학

초록

In this paper, we prove $L^{p}$ estimates of a class of singular integral operators on product domains along surfaces defined by mappings that are more general than polynomials and convex functions. We assume that the kernels are in $L(\log L)^{2}(\mathbb{S}^{n-1}\times \mathbb{S}^{m-1})$. Furthermore, we\ prove $L^{p}$ estimates of the related class of Marcinkiewicz integral operators. Our results extend as well as improve previously known results.

Abstract

In this paper, we prove $L^{p}$ estimates of a class of singular integral operators on product domains along surfaces defined by mappings that are more general than polynomials and convex functions. We assume that the kernels are in $L(\log L)^{2}(\mathbb{S}^{n-1}\times \mathbb{S}^{m-1})$. Furthermore, we\ prove $L^{p}$ estimates of the related class of Marcinkiewicz integral operators. Our results extend as well as improve previously known results.

참고문헌 (30)

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