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.
Original language | English |
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Journal | Journal of Approximation Theory |
Volume | 234 |
Pages (from-to) | 1-19 |
Number of pages | 19 |
ISSN | 0021-9045 |
DOIs | |
Publication status | Published - Oct 2018 |
Keywords
- Besov spaces
- distributions
- doubling property
- equivalent norms
- Hardy spaces
- Lipschitz spaces
- self-adjoint operators
- Sobolev spaces
- spaces of homogeneous type
- spectral multipliers
- Triebel–Lizorkin spaces