$Tb$ theorem for singular integral operators in the Dunkl setting

In this talk, we will discuss a $T_b$ theorem for a family of singular integral operators in the Dunkl setting. These operators, which generalize the Dunkl--Riesz transforms, have kernels satisfying estimates that lie outside the Coifman--Weiss framework for singular integral operators on general spaces of homogeneous type. In analogy with the $T_b$ theorem of David, Journé, and Semmes, our result establishes $L^2$ boundedness criteria via testing conditions against para-accretive functions adapted to the Dunkl structure. This is joint work with Francesco D'Emilio, Ji Li, and Brett Wick.