Sobolev-Type Inequalities for Dunkl Operators

Andrei Velicu

Published 2018-11-27Version 1

In this paper we study the Sobolev inequality in the Dunkl setting using two new approaches which provide a simpler elementary proof of the classical case $p=2$, as well as an extension to the coefficient $p=1$ that was previously unknown. We also find sharp constants for the Sobolev inequality in Weyl chambers and on the whole space $\mathbb{R}^N$.