Dispersive and Strichartz estimates on H-type groups
Volume 169 / 2005
Studia Mathematica 169 (2005), 1-20
MSC: 22E25, 17B70, 33C45, 35H20, 35B40.
DOI: 10.4064/sm169-1-1
Abstract
Our purpose is to generalize the dispersive inequalities for the wave equation on the Heisenberg group, obtained in \cite{BGX}, to H-type groups. On those groups we get optimal time decay for solutions to the wave equation (decay as $t^{-p/2}$) and the Schrödinger equation (decay as $t^{(1-p)/2}$), $p$ being the dimension of the center of the group. As a corollary, we obtain the corresponding Strichartz inequalities for the wave equation, and, assuming that $p>1$, for the Schrödinger equation.
