Rough Singular Integral Operators Along Submanifolds (Analysis in Theory and Applications, 2023)
This paper is a summary of the research on the mapping properties of singular integrals with rough kernels and the corresponding maximal operators. Moreprecisely, the author presents some recent progress, interesting problems and typical methods used in the theory concerning the boundedness and continuity for therough singular integral operators and maximal singular integral operators along certain submanifolds such as polynomial mappings, polynomial curves, homogeneousmappings, surfaces of revolution and real-analytic submanifolds on the Lebesguespaces, Triebel–Lizorkin spaces, Besov spaces and mixed radial-angular spaces.
Keywords: Singular integral; maximal singular integral; rough kernel; submanifolds.