Mixed radial‐angular integrability for rough maximal singular integrals and Marcinkiewicz integrals with mixed homogeneity

Abstract

This paper is devoted to studying maximal singular integrals and Marcinkiewicz integrals with rough kernels in a mixed homogeneity setting. Assuming that the kernels satisfy certain rather weak size conditions, the boundedness of such operators on the mixed radial-angular spaces are established, respectively. Meanwhile, the corresponding vector-valued versions are also given.