Power weighted L p -inequalities for Laguerre–Riesz transforms

We also show how one can use this abstract formulation both for giving different and sim- pler proofs for all the known results obtained for the eigenvalues of a power of the

[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

Taylor, Potential theory on Lipschitz domains in Riemannian manifolds: Sobolev-Besov space results and the Poisson problem, J. Pazy, Semigroups of Linear Operators and Applications

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

We prove new upper bounds for the first positive eigenvalue of a family of second order operators, including the Bakry- ´ Emery Laplacian, for submanifolds of weighted

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