Boundedness of admissible area function on nonisotropic Lipschitz space

Gao, Jinshou; Jia, Houyu

doi:10.1090/S0002-9939-04-07733-0

Boundedness of admissible area function on nonisotropic Lipschitz space
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by Jinshou Gao and Houyu Jia PDF

Proc. Amer. Math. Soc. 133 (2005), 1777-1785 Request permission

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 $\|S_\beta (f)\|_{Lip_\alpha }\le C \|f\|_{Lip_\alpha }$.

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