Hp-bounds for spectral multipliers on Riemannian manifolds
- Georgiadis, Athanasios G.
DOIAbstract
AbstractLet M be a Riemannian manifold which satisfies the doubling volume property. Let Δ be the Laplace–Beltrami operator on M and m(λ), λ∈R, a multiplier satisfying the Mikhlin–Hörmander condition. We also assume that the heat kernel satisfies certain upper Gaussian estimates and we prove that there is a geometric constant p0<1, such that the spectral multiplier m(Δ) is bounded on the Hardy spaces Hp for all p∈(p0,1]
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