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Singular and Marcinkiewicz integral operators on product domains
Badriya Al-Azri,Ahmad Al-Salman 대한수학회 2023 대한수학회논문집 Vol.38 No.2
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.
A Note on Marcinkiewicz Integral Operators on Product Domains
Badriya Al-Azri,Ahmad Al-Salman 경북대학교 자연과학대학 수학과 2023 Kyungpook mathematical journal Vol.63 No.4
In this paper we establish the Lp boundedness of Marcinkiewicz integral oper ators on product domains with rough kernels satisfying a weak size condition. We assume that our kernels are supported on surfaces generated by curves more general than polyno mials and convex functions. This generalizes and extends previous results.