Homogeneous algebras via heat kernel estimates
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- by Tommaso Bruno PDF
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Abstract:
We study homogeneous Besov and Triebel–Lizorkin spaces defined on doubling metric measure spaces in terms of a self-adjoint operator whose heat kernel satisfies Gaussian estimates together with its derivatives. When the measure space is a smooth manifold and such operator is a sum of squares of smooth vector fields, we prove that their intersection with $L^\infty$ is an algebra for pointwise multiplication. Our results apply to nilpotent Lie groups and Grushin settings.References
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Additional Information
- Tommaso Bruno
- Affiliation: Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, 9000 Ghent, Belgium
- Address at time of publication: Dipartimento di Matematica, Università degli Studi di Genova, Via Dodecaneso 35, 16146 Genova, Italy
- MR Author ID: 1213879
- ORCID: 0000-0001-7116-8044
- Email: brunot@dima.unige.it
- Received by editor(s): February 27, 2021
- Received by editor(s) in revised form: November 14, 2021
- Published electronically: July 25, 2022
- Additional Notes: The author was supported by the Research Foundation – Flanders (FWO) through the postdoctoral grant 12ZW120N. He was also partially supported by the GNAMPA 2020 project “Fractional Laplacians and subLaplacians on Lie groups and trees”.
- © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 375 (2022), 6903-6946
- MSC (2020): Primary 46E35, 58J35, 43A85; Secondary 46E36, 46F10, 22E25
- DOI: https://doi.org/10.1090/tran/8697