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

Athanasios G. Georgiadis (), Gérard Kerkyacharian, (), Georges Kyriazis () and Pencho Petrushev ()
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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

No 2017-92, Working Papers from Center for Research in Economics and Statistics

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.

Keywords: Heat kernel; Besov spaces; Triebel–Lizorkin spaces; Homogeneous spaces; Distributions; Generalized polynomials (search for similar items in EconPapers)
Pages: 31 pages
Date: 2017-05-15
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