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Some Function Spaces Relative to Morrey-Campanato Spaces on Metric Spaces

Published online by Cambridge University Press:  11 January 2016

Dachun Yang
Dachun Yang*
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, People’s, Republic of China, [email protected]
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Abstract

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In this paper, the author introduces the Morrey-Campanato spaces Lsp(X) and the spaces Cps(X) on spaces of homogeneous type including metric spaces and some fractals, and establishes some embedding theorems between these spaces under some restrictions and the Besov spaces and the Triebel-Lizorkin spaces. In particular, the author proves that Lsp(X) = Bs∞,∞(X) if 0 < s < ∞ and µ(X) < ∞. The author also introduces some new function spaces Asp(X) and Bsp(X) and proves that these new spaces when 0 < s < 1 and 1 < p < ∞ are just the Triebel-Lizorkin space Fsp,∞(X) if X is a metric space, and the spaces A1p(X) and B1p(X) when 1 < p < ∞ are just the Hajłasz-Sobolev spaces W1p(X). Finally, as an application, the author gives a new characterization of the Hajłasz-Sobolev spaces by making use of the sharp maximal function.

Keywords

42B3546E3543-99
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 177 , 2005 , pp. 1 - 29
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2005

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