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arXiv · 1210.6237

Heat kernel based decomposition of spaces of distributions in the framework of Dirichlet spaces

Gerard Kerkyacharian·Pencho Petrushev
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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 Poincaré inequality. This leads to Heat kernel with small time Gaussian bounds and Hölder 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.

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Gerard Kerkyacharian, Pencho Petrushev. 2014-06-08. Heat kernel based decomposition of spaces of distributions in the framework of Dirichlet spaces. https://arxiv.org/abs/1210.6237

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