Reversed Hardy-Littlewood-Sobolev inequalities with weights on the Heisenberg group

Abstract

In this article, we establish some reverse weighted Hardy-Littlewood-Sobolev inequalities on the Heisenberg group. We then show the existence of extremal functions for the above inequalities by combining the subcritical approach and the renormalization method.

Keywords

• reverse weighted hardy-littlewood-sobolev inequality
• heisenberg group
• extremal function
• renormalization method
• 35a23
• 45e10
• 45g15
• 43a85