Existence of Extremals of Dunkl-Type Sobolev Inequality and of Stein–Weiss Inequality for Dunkl Riesz Potential

Abstract

In this paper, we prove the existence of an extremal for the Dunkl-type Sobolev inequality in the case of $$p=2$$ . Also we prove the existence of an extremal of the Stein–Weiss inequality for the Dunkl Riesz potential in the case of $$r=2$$ .