Seminar
Abstract: In harmonic analysis, the study of multilinear operators plays a pivotal role in various fields such as partial differential equations, complex analysis, and quantum mechanics. This talk delves into the boundedness of certain multilinear operators within the framework of Dunkl Fourier analysis, a parallel theory to classical Fourier analysis associated with root systems and reflection groups.
We begin by exploring the weighted boundedness of multilinear Calderón-Zygmund type singular integral operators. These operators, defined with respect to the Dunkl metric and the usual metric, represent a different class of operators from the classical Calderón-Zygmund operators. We establish one and two-weight estimates for these operators and associated maximal operators, showcasing their importance in the Dunkl framework.