A note on commutators of singular integrals with BMO and VMO functions in the Dunkl setting

Abstract

AbstractOn equipped with a root system R, multiplicity function , and the associated measure , we consider a (nonradial) kernel , which has properties similar to those from the classical theory of singular integrals and the Dunkl convolution operator associated with K. Assuming that b belongs to the BMO space on the space of homogeneous type , we prove that the commutator is a bounded operator on for all . Moreover, is compact on , provided . The paper extends results of Han, Lee, Li, and Wick.