A Theory of Besov and Triebel-Lizorkin Spaces on Metric Measure Spaces Modeled on Carnot-Carathéodory SpacesReportar como inadecuado




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Abstract and Applied Analysis - Volume 2008 2008, Article ID 893409, 250 pages

Research Article

Department of Mathematics, Auburn University, Auburn, AL 36849-5310, USA

Mathematisches Seminar, Christian-Albrechts-Universität Kiel, Ludewig-Meyn Strasse 4, 24098 Kiel, Germany

School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China

Received 13 February 2008; Accepted 23 May 2008

Academic Editor: Stephen Clark

Copyright © 2008 Yongsheng Han et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We work on RD-spaces 𝒳, namely, spaces of homogeneous type in thesense of Coifman and Weiss with the additional property that a reverse doubling property holds in 𝒳. An important example is the Carnot-Carathéodoryspace with doubling measure. By constructing an approximation of the identity with bounded support of Coifman type, we develop a theory of Besovand Triebel-Lizorkin spaces on the underlying spaces. In particular, thisincludes a theory of Hardy spaces Hp𝒳 and local Hardy spaces hp𝒳 on RD-spaces, which appears to be new in this setting. Among other things, wegive frame characterization of these function spaces, study interpolation ofsuch spaces by the real method, and determine their dual spaces when p≥1.The relations among homogeneous Besov spaces and Triebel-Lizorkin spaces,inhomogeneous Besov spaces and Triebel-Lizorkin spaces, Hardy spaces, andBMO are also presented. Moreover, we prove boundedness results on theseBesov and Triebel-Lizorkin spaces for classes of singular integral operators,which include non-isotropic smoothing operators of order zero in the sense ofNagel and Stein that appear in estimates for solutions of the Kohn-Laplacianon certain classes of model domains in ℂN. Our theory applies in a widerange of settings.





Autor: Yongsheng Han, Detlef Müller, and Dachun Yang

Fuente: https://www.hindawi.com/



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