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Generalized Gaussian estimates and riesz means of Schrödinger groups

Part of: Abstract harmonic analysis General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

Sönke Blunck
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Abstract

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We show that generalized Gaussian estimates for selfadjoint semigroups (e-tA)t ∈ R+ on L2 imply Lp boundedness of Riesz means and other regularizations of the Schrödinger group (eitA)t ∈ R. This generalizes results restricted to semigroups with a heat kernel, which are due to Sjöstrand, Alexopoulos and more recently Carron, Coulhon and Ouhabaz. This generalization is crucial for elliptic operators A that are of higher order or have singular lower order terms since, in general, their semigroups fail to have a heat kernel.

MSC classification

Secondary: 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc. 47A60: Functional calculus
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 82 , Issue 2 , April 2007 , pp. 149 - 162
Copyright
Copyright © Australian Mathematical Society 2007

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