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Journal of Fourier Analysis and Applications

, Volume 25, Issue 6, pp 3259–3309 | Cite as

Atomic and Molecular Decomposition of Homogeneous Spaces of Distributions Associated to Non-negative Self-Adjoint Operators

  • A. G. GeorgiadisEmail author
  • G. Kerkyacharian
  • G. Kyriazis
  • P. Petrushev
Article
  • 46 Downloads

Abstract

We deal with homogeneous Besov and Triebel–Lizorkin spaces in the setting of a doubling metric measure space in the presence of a non-negative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. The class of almost diagonal operators on the associated sequence spaces is developed and it is shown that this class is an algebra. The boundedness of almost diagonal operators is utilized for establishing smooth molecular and atomic decompositions for the above homogeneous Besov and Triebel–Lizorkin spaces. Spectral multipliers for these spaces are established as well.

Keywords

Algebra Almost diagonal operators Atomic decomposition Besov spaces Frames Heat kernel Homogeneous spaces Molecular decomposition Spectral multipliers Triebel–Lizorkin spaces 

Mathematics Subject Classification

Primary 58J35 46E35 43A85 Secondary 42B25 42B15 42C15 42C40 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • A. G. Georgiadis
    • 1
    Email author
  • G. Kerkyacharian
    • 2
    • 3
  • G. Kyriazis
    • 1
  • P. Petrushev
    • 4
  1. 1.Department of Mathematics and StatisticsUniversity of CyprusNicosiaCyprus
  2. 2.Laboratoire de Probabilités et Modèles Aléatoires, CNRS-UMR 7599ParisFrance
  3. 3.CrestMalakoffFrance
  4. 4.Department of MathematicsUniversity of South CarolinaColumbiaUSA

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