On the representing measures of Dunkl’s intertwining operator

Abstract A distribution estimate for the representing measures of Dunkl’s intertwining operator is proved, by which some lower estimates sharper in some senses than those known for the Dunkl kernel, the associated heat kernel, and the associated Poisson kernel are obtained. We also prove some distribution estimates for the representing measures of the Dunkl-type generalized translation of radial functions.