H 1 − L 1 boundedness of Riesz transforms on Riemannian manifolds and on graphs

Emmanuel Russ (1)

1 IF - Institut Fourier

We prove that the Riesz transforms are bounded from H 1 to L 1 on complete Riemannian manifolds and on graphs with the doubling property and the Poincaré inequality.

Mots clés: 42B30; 58G11; Riesz transforms; heat kernel; Markov kernel; H 1; Hörmander integral condition

Domaines: Analyse classique [math.CA]

Emmanuel Russ. H 1 − L 1 boundedness of Riesz transforms on Riemannian manifolds and on graphs. Potential Analysis, 2001, 14, pp.301-330. ⟨hal-01617991⟩