H1-boundedness of Riesz transforms and imaginary powers of the Laplacian on Riemannian manifolds

Michel Marias; Emmanuel Russ

doi:10.1007/bf02384571

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H1-boundedness of Riesz transforms and imaginary powers of the Laplacian on Riemannian manifolds

Michel Marias Emmanuel Russ

Year: 2003 Journal: Arkiv för matematik Vol: 41 (1)Pages: 115-132 Publisher: Mittag-Leffler Institute

DOI: 10.1007/bf02384571

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Abstract

We prove that the linearized Riesz transforms and the imaginary powers of the Laplacian are H<sup>1</sup>-bounded on complete Riemannian manifolds satisfying the doubling property and the Poincaré inequality, where H<sup>1</sup> denotes the Hardy space on M.

Keywords:

Riesz transform Mathematics Bounded function The Imaginary Pure mathematics Laplace operator Space (punctuation) Riemannian manifold Mathematical analysis Linguistics

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Advanced Harmonic Analysis Research

Physical Sciences → Mathematics → Applied Mathematics

Geometric Analysis and Curvature Flows

Physical Sciences → Mathematics → Applied Mathematics

Nonlinear Partial Differential Equations

Physical Sciences → Mathematics → Applied Mathematics

H1-boundedness of Riesz transforms and imaginary powers of the Laplacian on Riemannian manifolds

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