Indefinite higher Riesz transforms

More generally, using an analogue of Funk- Hecke formula for h-harmonics we can show that the mixed norm estimates for the Riesz transforms R κ j are equivalent to a vector

[2] to Riemannian manifolds of homogeneous type with polynomial volume growth where Poincar´e inequalities hold and Riesz transforms associated to the Laplace-Beltrami operator

Muckenhoupt weights, weighted Hardy spaces, atomic decompo- sition, molecular characterization, Riesz transforms, Calder´ on-Zygmund

We also obtain another characterization of the validity of (R p ) for p > 2 in terms of reverse H¨ older inequalities for the gradient of harmonic functions, in the spirit of

Carron, In´ egalit´ es isop´ erim´ etriques de Faber-Krahn et cons´ equences, in Actes de la table ronde de g´ eom´ etrie diff´ erentielle (Luminy, 1992), S´ emin. Carron, Une

Key words: elliptic operators, divergence form, semigroup, L p estimates, Calder´on-Zygmund theory, good lambda inequalities, hypercontractivity, Riesz transforms,

Here, we study weighted norm inequalities for the Riesz transform of the Laplace-Beltrami operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under

In the last section we prove Theorem 1.3 ; one of the main ingredient is to prove that if the manifold M satisfies condition (1), then R − satisfies (S-C) if and only if condition