Sharp Hardy-Rellich Type Inequalities Associated with Dunkl Operators

Abstract

In this paper, we obtained the Dunkl analogy of classical Lp Hardy inequality for $p>N+2\gamma$ with sharp constant ${\left(\frac{p-N-2\gamma }{p}\right)}^p$, where $2\gamma$ is the degree of weight function associated with Dunkl operators, and $L^p$ Hardy inequalities with distant function in some G-invariant domains. Moreover we proved two sharp Hardy-Rellich type inequalities for Dunkl operators.