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Dispersive and Strichartz estimates on H-type groups

Martin Del Hierro — 2005

Studia Mathematica

Our purpose is to generalize the dispersive inequalities for the wave equation on the Heisenberg group, obtained in [1], 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.

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