Spectral multipliers on spaces of distributions associated with non-negative self-adjoint operators

Athanasios Georgiadis, Morten Nielsen

Research output: Contribution to journalJournal articleResearchpeer-review

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 languageEnglish
JournalJournal of Approximation Theory
Volume234
Pages (from-to)1-19
Number of pages19
ISSN0021-9045
DOIs
Publication statusPublished - Oct 2018

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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

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