Decay estimates for fractional wave equations on H-type groups

TL;DR

This paper establishes decay estimates and Strichartz inequalities for fractional wave equations on H-type groups, extending understanding of dispersive properties in this geometric setting.

Contribution

It provides the first decay estimates and Strichartz inequalities for fractional wave equations on H-type groups, combining dispersive analysis with duality methods.

Findings

Decay estimates for fractional wave semigroup on H-type groups.

Strichartz inequalities derived for the fractional wave equation.

Enhanced understanding of dispersive behavior in non-commutative geometric settings.

Abstract

The aim of this paper is to establish the decay estimate for the fractional wave equation semigroup on H-type groups given by $e^{it\Delta^\alpha}$, $0<\alpha<1$. Combing the dispersive estimate and a standard duality argument, we also derive the corresponding Strichartz inequalties.