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Boundedness of admissible area function on nonisotropic Lipschitz space
Authors:Jinshou Gao  Houyu Jia
Institution:Department of Mathematics, Fujian Normal University, Fuzhou, 350007, People's Republic of China ; Department of Mathematics, Zhejiang University, Hangzhou, 310028, People's Republic of China
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 $\Vert S_\beta (f)\Vert _{Lip_\alpha}\le C \Vert f\Vert _{Lip_\alpha}$.

Keywords:Unit ball in $C^n$  admissible area function  nonisotropic Lipschitz space
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