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Boundedness of admissible area function on nonisotropic Lipschitz space

Author(s): Jinshou Gao; Houyu Jia
Journal: Proc. Amer. Math. Soc. 133 (2005), 1777-1785.
MSC (2000): Primary 47B38, 32A37, 42B25
Posted: December 20, 2004
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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: 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
Posted: December 20, 2004
Additional Notes: The second author was supported in part by the Education Department of Zhejiang Province
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2004, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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