The Dunkl operators are substitutes of differential operators involving reflection terms, which are connected with Coxeter groups and root systems. In this talk we shall introduce our recent research on the boundary behaviour of generalized harmonic functions associated with the Dunkl operators.  The main results are about characterizations on local existence of non-tangential boundary values of generalized harmonic functions, which are given by non-tangential boundedness of functions and finiteness of a Lusin-type area integral in the Dunkl setting.

海报