Some Estimates for $θ$-Type Calderόn–Zygmund Operators and Linear Commutators on Certain Weighted Amalgam Spaces (Analysis in Theory and Applications, 2023)
In this paper, we first introduce some new kinds of weighted amalgamspaces. Then we discuss the strong type and weak type estimates for a class ofCalderόn–Zygmund type operators $T_θ$ in these new weighted spaces. Furthermore,the strong type estimate and endpoint estimate of linear commutators $[b, T_θ]$ formedby $b$ and $T_θ$ are established. Also we study related problems about two-weight, weaktype inequalities for $T_θ$ and $[b, T_θ]$ in the weighted amalgam spaces and give someresults.
Keywords: $θ$-type Calderόn–Zygmund operators; commutators; weighted amalgam spaces; Muckenhoupt weights; Orlicz spaces.