Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898408 | Journal of Approximation Theory | 2018 | 20 Pages |
Abstract
We consider spaces of homogeneous type associated with a non-negative self-adjoint operator whose heat kernel satisfies certain upper Gaussian bounds. Spectral multipliers are introduced and studied on distributions associated with this operator. The boundedness of spectral multipliers on Besov and Triebel-Lizorkin spaces with full range of indices is established too. As an application, we obtain equivalent norm characterizations for the spaces mentioned above. Non-classical spaces as well as Lebesgue, Hardy, (generalized) Sobolev and Lipschitz spaces are also covered by our approach.
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
Athanasios G. Georgiadis, Morten Nielsen,