Abstract
The aim of this paper is to establish the decay estimate for the fractional wave equation semigroup on H-type groups given by $e^{it\Delta^{\alpha}}$ , $0<\alpha<1$ . Combining the dispersive estimate and a standard duality argument, we also derive the corresponding Strichartz inequalities.
Highlights
1 Introduction In this paper, we study the decay estimate for a class of dispersive equations: i∂tu + αu = f, u( ) = u, ( )
Let N be the homogeneous dimension of the H-type group G, and p the dimension of its center
On H-type group G, there is a relation between the dimension of the center and its orthogonal complement space
Summary
In , Bahouri et al [ ] derived the Strichartz inequalities for the wave equation on the Heisenberg group via a sharp dispersive estimate and a standard duality argument The sharp dispersive estimate is generalized to H-type groups for the wave equation and the Schrödinger equation (see [ – ]). Motivated by Guo et al [ ] on the Euclidean space, we consider the fractional wave equation ( ) on H-type groups and will prove a sharp dispersive estimate. Let N be the homogeneous dimension of the H-type group G, and p the dimension of its center.
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