Some Estimates for $θ$-type Calderόn–Zygmund Operators and Linear Commutators on Certain Weighted Amalgam Spaces

Abstract

In this paper, we first introduce some new kinds of weighted amalgam spaces. Then we discuss the strong type and weak type estimates for a class of Calderón–Zygmund type operators Tθ in these new weighted spaces. Furthermore, the strong type estimate and endpoint estimate of linear commutators [b, Tθ ] formed by b and Tθ are established. Also we study related problems about two-weight, weak type inequalities for Tθ and [b, Tθ ] in the weighted amalgam spaces and give some results.