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Pré-Publication, Document De Travail Année : 2022

REVERSE INEQUALITY FOR THE RIESZ TRANSFORMS ON RIEMANNIAN MANIFOLDS

Emmanuel Russ
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Résumé

Let M be a complete Riemannian manifold satisfying the doubling volume condition for geodesic balls and L^q scaled Poincaré inequalities on suitable remote balls for some q<2. We prove the inequality $||\Delta^{1/2}f||_p\lesssim ||\nabla f||_p$ for all p ∈ (q, 2], which generalizes previous results due to Auscher and Coulhon. Our conclusion applies, in particular, when M has a finite number of Euclidean ends. The proof strongly relies on Hardy inequalities, which are also new in this context and of independent interest.
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hal-03773356 , version 1 (09-09-2022)

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Emmanuel Russ, Baptiste Devyver. REVERSE INEQUALITY FOR THE RIESZ TRANSFORMS ON RIEMANNIAN MANIFOLDS. 2022. ⟨hal-03773356⟩
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