Hardy type spaces on certain noncompact manifolds and applications
Abstract
In this paper we consider a complete connected noncompact Riemannian manifold M with Ricci curvature bounded from below, positive injectivity radius and spectral gap b. We introduce a sequence X^1(M), X^2(M), ... of new Hardy spaces on M, the sequence Y^1(M/, Y^2(M), ... of their dual spaces, and show that these spaces may be used to obtain endpoint estimates for purely imaginary powers of the Laplace-Beltrami operator and for more general spectral multipliers associated to the Laplace--Beltrami operator L on M. Under the additional condition that the volume of the geodesic balls of radius r is controlled by C r^a e^{2\sqrt{b} r} for some real number a and for all large r, we prove also an endpoint result for first order Riesz transforms D L^{-1/2}. In particular, these results apply to Riemannian symmetric spaces of the noncompact type.
Cite
@article{arxiv.0812.4209,
title = {Hardy type spaces on certain noncompact manifolds and applications},
author = {G. Mauceri and S. Meda and M. Vallarino},
journal= {arXiv preprint arXiv:0812.4209},
year = {2014}
}
Comments
27 pages, v2: the first version has been revised and rearranged, with additions, in two papers, of which this new version is the first. The second paper is posted as arXiv:1002.1161v1