A note on commutators on weighted Morrey spaces on spaces of homogeneous type

Abstract

In this paper we study the boundedness and compactness characterizations of the commutator of Calderón-Zygmund operators $T$ on spaces of homogeneous type $(X,d,\mu )$ in the sense of Coifman and Weiss. More precisely, We show that the commutator $[b,T]$ is bounded on weighted Morrey space $L_{\omega }^{p,\kappa }(X)$ ($\kappa \in (0,1),\omega \in A_p(X),1<p<\infty$) if and only if $b$ is in the BMO space. Moreover, the commutator $[b,T]$ is compact on weighted Morrey space $L_{\omega }^{p,\kappa }(X)$ ($\kappa \in (0,1),\omega \in A_p(X),1<p<\infty$) if and only if $b$ is in the VMO space.

References in corpus (1)

• Cauchy-Szegö operator, quaternionic Siegel upper half space, commutator, weighted Morrey space