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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Boundedness of admissible area function on nonisotropic Lipschitz space


Authors: Jinshou Gao and Houyu Jia
Journal: Proc. Amer. Math. Soc. 133 (2005), 1777-1785
MSC (2000): Primary 47B38, 32A37, 42B25
Published electronically: December 20, 2004
MathSciNet review: 2120278
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Abstract: Let $B$ be the unit ball in $C^n$, let $S$ be the unit sphere, and let $S_\beta (f)$ be the admissible area function. In this paper, we show that if $f\in Lip_\alpha (S)$, then $S_\beta (f)\in Lip_\alpha (S)$ and there exists a constant $C$ such that $\Vert S_\beta (f)\Vert _{Lip_\alpha}\le C \Vert f\Vert _{Lip_\alpha}$.


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Additional Information

Jinshou Gao
Affiliation: Department of Mathematics, Fujian Normal University, Fuzhou, 350007, People’s Republic of China
Address at time of publication: Department of Mathematics, Zhejiang University, Hangzhou, 310028, People’s Republic of China
Email: gaojinshou@yahoo.com.cn

Houyu Jia
Affiliation: Department of Mathematics, Zhejiang University, Hangzhou, 310028, People’s Republic of China
Email: mjhy@zju.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07733-0
PII: S 0002-9939(04)07733-0
Keywords: Unit ball in $C^n$, admissible area function, nonisotropic Lipschitz space
Received by editor(s): September 17, 2003
Received by editor(s) in revised form: February 20, 2004
Published electronically: December 20, 2004
Additional Notes: The second author was supported in part by the Education Department of Zhejiang Province
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.