Heat kernel based decomposition of spaces of distributions in the framework of Dirichlet spaces
Functional Analysis
2014-06-10 v2
Abstract
Classical and non classical Besov and Triebel-Lizorkin spaces with complete range of indices are developed in the general setting of Dirichlet space with a doubling measure and local scale-invariant Poincar\'e inequality. This leads to Heat kernel with small time Gaussian bounds and H\"older continuity, which play a central role in this article. Frames with band limited elements of sub-exponential space localization are developed, and frame and heat kernel characterizations of Besov and Triebel-Lizorkin spaces are established. This theory, in particular, allows to develop Besov and Triebel-Lizorkin spaces and their frame and heat kernel characterization in the context of Lie groups, Riemannian manifold, and other settings.
Cite
@article{arxiv.1210.6237,
title = {Heat kernel based decomposition of spaces of distributions in the framework of Dirichlet spaces},
author = {Gerard Kerkyacharian and Pencho Petrushev},
journal= {arXiv preprint arXiv:1210.6237},
year = {2014}
}