Two-Weight, Weak-Type Norm Inequalities for a Class of Sublinear Operators on Weighted Morrey and Amalgam Spaces

Abstract

Let Tα0≤α<n be a class of sublinear operators satisfying certain size conditions introduced by Soria and Weiss, and let b,Tα0≤α<n be the commutators generated by BMORn functions and Tα. This paper is concerned with two-weight, weak-type norm estimates for these sublinear operators and their commutators on the weighted Morrey and amalgam spaces. Some boundedness criteria for such operators are given, under the assumptions that weak-type norm inequalities on weighted Lebesgue spaces are satisfied. As applications of our main results, we can obtain the weak-type norm inequalities for several integral operators as well as the corresponding commutators in the framework of weighted Morrey and amalgam spaces.