Some estimates for commutators of Calder\'on-Zygmund operators on the weighted Morrey spaces

TL;DR

This paper investigates the boundedness of commutators of Calderón-Zygmund operators on weighted Morrey spaces, establishing new weighted boundedness results under specific conditions on the weight and symbol functions.

Contribution

It provides new weighted boundedness properties of commutators of Calderón-Zygmund operators on weighted Morrey spaces, extending previous results to broader function spaces.

Findings

Weighted boundedness of commutators $[b,T]$ on $L^{p,\, ext{κ}}(w)$

Conditions on weights $w$ for boundedness

Results for symbols in weighted BMO and Lipschitz spaces

Abstract

Let $T$ be a Calder\'on-Zygmund singular integral operator. In this paper, we will show some weighted boundedness properties of commutator $[b,T]$ on the weighted Morrey spaces $L^{p,\kappa}(w)$ under appropriate conditions on the weight $w$, where the symbol $b$ belongs to weighted $BMO$ or Lipschitz space or weighted Lipschitz space.