Multilinear Strongly Singular Integral Operators with Generalized Kernels on RD-Spaces (2412.18392v1)

Abstract: In this article, we introduce a class of multilinear strongly singular integral operators with generalized kernels on the RD-space. The boundedness of these operators on weighted Lebesgue spaces is established. Moreover, two types of endpoint estimates and their boundedness on generalized weighted Morrey spaces are obtained. Our results further generalize the relevant conclusions on generalized kernels in Euclidean spaces. Moreover, the weak-type results on weighted Lebesgue spaces are brand new even in the situation of Euclidean spaces. In addition, when the generalized kernels degenerate into classical kernels, our research results also extend the relevant known results. It is worth mentioning that our RD spaces are more general than theirs.