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L ∞ — Decay estimations of the spherical mean value on symmetric spaces

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Abstract

LetM t[ϕ](x) be the spherical mean value operator applied to a function ϕ on a symmetric Riemannian space of the non-compact type.L ∞ —decay estimations forM t [ϕ](x) as well as for its derivatives with respect to (t, x) are given, provided that ϕ belongs to a Banach space with suitable weighted supremum norm. This leads to estimates of the solutions to the wave equation in certain cases in which Huygens' principle is valid.

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  1. Institut für Mathematik, Universität Leipzig, Augustusplatz 10, 04109, Leipzig, Germany

    Paul Günther

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  1. Paul Günther
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Günther, P. L ∞ — Decay estimations of the spherical mean value on symmetric spaces. Ann Glob Anal Geom 12, 219–236 (1994). https://doi.org/10.1007/BF02108299

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