An extension problem and trace Hardy inequality for the sublaplacian on $H$-type groups

TL;DR

This paper investigates the extension problem for the sublaplacian on H-type groups and establishes trace Hardy and Hardy inequalities for fractional powers, advancing understanding of these inequalities in non-commutative geometric settings.

Contribution

It introduces new trace Hardy inequalities for fractional sublaplacians on H-type groups, extending classical results to a broader non-commutative context.

Findings

Proved trace Hardy inequalities for fractional sublaplacians.

Established extension problem solutions on H-type groups.

Extended classical Hardy inequalities to non-commutative groups.

Abstract

In this paper we study the extension problem for the sublaplacian on a $H$-type group and use the solutions to prove trace Hardy and Hardy inequalities for fractional powers of the sublaplacian.