Vector-valued estimates on limiting weak-type behaviors of singular integrals and maximal operators

Abstract

This paper is devoted to studying the vector-valued estimates for the limiting weak-type behaviors of singular and fractional integrals as well as maximal operators with homogeneous kernels. Under the assumptions of that the kernels satisfy certain Dini-type conditions, the limiting weak-type behaviors for the corresponding vector-valued operators are given. Our results imply that the classical vector-valued weak-type endpoint estimates for singular and fractional integrals or maximal operators are not sharp.