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-bounds for spectral multipliers on Riemannian manifolds

✍ Scribed by Athanasios G. Georgiadis

Publisher
Elsevier Science
Year
2010
Tongue
French
Weight
163 KB
Volume
134
Category
Article
ISSN
0007-4497

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✦ Synopsis

Let M be a Riemannian manifold which satisfies the doubling volume property. Let be the Laplace-Beltrami operator on M and m(λ), λ ∈ R, a multiplier satisfying the Mikhlin-Hârmander condition. We also assume that the heat kernel satisfies certain upper Gaussian estimates and we prove that there is a geometric constant p 0 < 1, such that the spectral multiplier m( ) is bounded on the Hardy spaces H p for all p ∈ (p 0 , 1].

πŸ“œ SIMILAR VOLUMES

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✍ Harold Donnelly πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 188 KB

Suppose that f is an eigenfunction of -D with eigenvalue l ] 0. It is proved that where n is the dimension of M and c 1 depends only upon a bound for the absolute value of the sectional curvature of M and a lower bound for the injectivity radius of M. It is then shown that if M admits an isometric