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

2012

109 citations recorded by the source corpus.

Classical and nonclassical 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 Poincare inequality. This leads to a heat kernel with small time Gaussian bounds and Holder 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 the development of Besov and Triebel-Lizorkin spaces and their frame and heat kernel characterization in the context of Lie groups, Riemannian manifolds, and other settings.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/f46f5865549e3b3caa9aa853dbf37f9abd9a93c2

Citations in the corpus

• Wavelet transforms for homogeneous mixed-norm Triebel–Lizorkin spaces (2016, unknown): “For spaces on other domains such as the sphere, see for example [18, 25, 26, 29, 30].”
• Besov and Triebel-Lizorkin Spaces Associated to Hermite Operators (2015, unknown): “Moreover, in comparison with the results in [10,12], the molecular decompositions and the theory of Besov and Triebel–Lizorkin spaces are new.”
• Pseudodifferential operators on mixed‐norm Besov and Triebel–Lizorkin spaces (2016, unknown): “See for example [15], [16], [19] and the references therein.”