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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Homogeneous algebras via heat kernel estimates
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by Tommaso Bruno PDF
Trans. Amer. Math. Soc. 375 (2022), 6903-6946 Request permission


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.
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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:
  • 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: