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1995 Some estimates related to fractal measures and Laplacians on manifolds
Limin Sun
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Ark. Mat. 33(1): 173-182 (1995). DOI: 10.1007/BF02559609

Abstract

Let $\Delta$ be the Laplace-Beltrami operator on an $n$-dimensional complete $C^∞$ manifold $M$. In this paper, we establish an estimate of $e^{t\Delta} (d\mu)$ valid for all $t \gt 0$, where $d\mu$ is a locally uniformly $\alpha$-dimensional measure on $M, 0 ≤ \alpha ≤ n$. The result is used to study the mapping properties of $(I - t\Delta)^{-\beta}$ considered as an operator from $L^p (M, d\mu)$ to $L^p (M, dx)$, where $dx$ is the Riemannian measure on $M$, $\beta \gt (n−\alpha)/2p′, 1/p+1/p′=1, 1≤ p ≤ ∞$.

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Limin Sun. "Some estimates related to fractal measures and Laplacians on manifolds." Ark. Mat. 33 (1) 173 - 182, 1995. https://doi.org/10.1007/BF02559609

Information

Received: 4 November 1992; Published: 1995
First available in Project Euclid: 31 January 2017

zbMATH: 0839.58054
MathSciNet: MR1340274
Digital Object Identifier: 10.1007/BF02559609

Rights: 1995 © Institut Mittag Leffler

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Vol.33 • No. 1 • 1995
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