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Homogeneous Besov and Triebel–Lizorkin spaces associated tonon-negative self-adjoint operators

Author

Listed:
  • Athanasios G. Georgiadis

    (Department of Mathematical Sciences; Aalborg University)

  • Gérard Kerkyacharian,

    (Laboratoire de Probabilités et Modèles aléatoires; Université Paris VII)

  • Georges Kyriazis

    (University of Cyprus)

  • Pencho Petrushev

    (University of South Carolina; Interdisciplinary Mathematics Institute)

Abstract

Homogeneous Besov and Triebel–Lizorkin spaces with complete set of indices are introduced in the general 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 main step in this theory is the development of distributions modulo generalized polynomials. Some basic properties of the general homogeneous Besov and Triebel–Lizorkin spaces are established, in particular, adiscrete (frame) decomposition of these spaces is obtained.

Suggested Citation

  • Athanasios G. Georgiadis & Gérard Kerkyacharian, & Georges Kyriazis & Pencho Petrushev, 2017. "Homogeneous Besov and Triebel–Lizorkin spaces associated tonon-negative self-adjoint operators," Working Papers 2017-92, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2017-92
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