Journal of Operator Theory

Volume 53, Issue 2, Spring 2005 pp. 351-365.

Generalized Gaussian estimates and the Legendre transform

Authors: S. Blunck (1) and P.C. Kunstmann (2)
Author institution: (1) Universit\'e de Cergy-Pontoise, D\'epartement de Math\'ematiques, 2, avenue Adolphe Chauvin, 95302 Cergy-Pontoise, France
(2) Universit\"at Karlsruhe, Mathematisches Institut I, Englerstr. 2, 76128 Karlsruhe, Germany

Summary: Generalized Gaussian estimates (GGEs) are the main tool for the $L_p$-extension of $L_2$-properties of elliptic operators without heat kernel, e.g. operators of higher order and operators with complex or unbounded coefficients. In this paper, we give several characterizations of GGEs which are important for the applicability of such $L_p$-extension results. As an application of these characterizations, we show a result on the spectral $L_p$-independence of operators satisfying GGEs.

Keywords: Generalized Gaussian estimates, elliptic operator, heat kernel.

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