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A Theory of Besov and Triebel-Lizorkin Spaces on Metric Measure Spaces Modeled on Carnot-Carathéodory Spaces
Joint Authors
Müller, Detlef
Han, Yongsheng
Yang, Dachun
Source
Issue
Vol. 2008, Issue 2008 (31 Dec. 2008), pp.1-250, 250 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-03-04
Country of Publication
Egypt
No. of Pages
250
Main Subjects
Abstract EN
We work on RD-spaces ?, namely, spaces of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in ?.
An important example is the Carnot-Carathéodory space with doubling measure.
By constructing an approximation of the identity with bounded support of Coifman type, we develop a theory of Besov and Triebel-Lizorkin spaces on the underlying spaces.
In particular, this includes a theory of Hardy spaces Hp(?) and local Hardy spaces hp(?) on RD-spaces, which appears to be new in this setting.
Among other things, we give frame characterization of these function spaces, study interpolation of such 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, and BMO are also presented.
Moreover, we prove boundedness results on these Besov and Triebel-Lizorkin spaces for classes of singular integral operators, which include non-isotropic smoothing operators of order zero in the sense of Nagel and Stein that appear in estimates for solutions of the Kohn-Laplacian on certain classes of model domains in ℂN.
Our theory applies in a wide range of settings.
American Psychological Association (APA)
Han, Yongsheng& Müller, Detlef& Yang, Dachun. 2009. A Theory of Besov and Triebel-Lizorkin Spaces on Metric Measure Spaces Modeled on Carnot-Carathéodory Spaces. Abstract and Applied Analysis،Vol. 2008, no. 2008, pp.1-250.
https://search.emarefa.net/detail/BIM-506016
Modern Language Association (MLA)
Han, Yongsheng…[et al.]. A Theory of Besov and Triebel-Lizorkin Spaces on Metric Measure Spaces Modeled on Carnot-Carathéodory Spaces. Abstract and Applied Analysis No. 2008 (2008), pp.1-250.
https://search.emarefa.net/detail/BIM-506016
American Medical Association (AMA)
Han, Yongsheng& Müller, Detlef& Yang, Dachun. A Theory of Besov and Triebel-Lizorkin Spaces on Metric Measure Spaces Modeled on Carnot-Carathéodory Spaces. Abstract and Applied Analysis. 2009. Vol. 2008, no. 2008, pp.1-250.
https://search.emarefa.net/detail/BIM-506016
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-506016