Year: 2023
Author: Feng Liu
Analysis in Theory and Applications, Vol. 39 (2023), Iss. 3 : pp. 201–243
Abstract
This paper is a summary of the research on the mapping properties of singular integrals with rough kernels and the corresponding maximal operators. More precisely, the author presents some recent progress, interesting problems and typical methods used in the theory concerning the boundedness and continuity for the rough singular integral operators and maximal singular integral operators along certain submanifolds such as polynomial mappings, polynomial curves, homogeneous mappings, surfaces of revolution and real-analytic submanifolds on the Lebesgue spaces, Triebel–Lizorkin spaces, Besov spaces and mixed radial-angular spaces.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-0025
Analysis in Theory and Applications, Vol. 39 (2023), Iss. 3 : pp. 201–243
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 43
Keywords: Singular integral maximal singular integral rough kernel submanifolds.