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Boundedness of admissible area function on nonisotropic Lipschitz space
Authors:Jinshou Gao   Houyu Jia
Affiliation: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 $fin Lip_alpha (S)$, then $S_beta (f)in Lip_alpha (S)$ and there exists a constant $C$ such that $Vert S_beta (f)Vert _{Lip_alpha}le C Vert fVert _{Lip_alpha}$.

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