This paper is a summary of the research on the mapping properties of sin-gular integrals with rough kernels and the corresponding maximal operators.More precisely,the author presents some recent progress,interesting p...This paper is a summary of the research on the mapping properties of sin-gular integrals with rough kernels and the corresponding maximal operators.More precisely,the author presents some recent progress,interesting problems and typi-cal methods used in the theory concerning the boundedness and continuity for the rough singular integral operators and maximal singular integral operators along cer-tain 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.展开更多
基金survey report given in the Workshop on Operators with Rough Kernels in China(Jinhua,July 15-18,2022)supported partly by the National Natural Sci-ence Foundation of China(Grant No.11701333)。
文摘This paper is a summary of the research on the mapping properties of sin-gular integrals with rough kernels and the corresponding maximal operators.More precisely,the author presents some recent progress,interesting problems and typi-cal methods used in the theory concerning the boundedness and continuity for the rough singular integral operators and maximal singular integral operators along cer-tain 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.
