Dispersive and Strichartz estimates on H-type groups

Martin Del Hierro

Studia Mathematica, Tome 166 (2005), p. 1-20 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Publié le : 2005-01-01

Zbl 1076.22010

EUDML-ID : urn:eudml:doc:285286

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     title = {Dispersive and Strichartz estimates on H-type groups},
     journal = {Studia Mathematica},
     volume = {166},
     year = {2005},
     pages = {1-20},
     zbl = {1076.22010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-1-1}
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Martin Del Hierro. Dispersive and Strichartz estimates on H-type groups. Studia Mathematica, Tome 166 (2005) pp. 1-20. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-1-1/