HOLOMORPHIC MEAN LIPSCHITZ FUNCTIONS ON THE UNIT BALL OF ℂn

Title & Authors
HOLOMORPHIC MEAN LIPSCHITZ FUNCTIONS ON THE UNIT BALL OF ℂn
Kwon, Ern Gun; Cho, Hong Rae; Koo, Hyungwoon;

Abstract
On the unit ball of $\small{\mathbb{C}^n}$, the space of those holomorphic functions satisfying the mean Lipschitz condition $\small{{\int}_0^1\;{\omega}_p(t,f)^q\frac{dt}{t^1+{\alpha}q}\;}$<$\small{\;{\infty}}$ is characterized by integral growth conditions of the tangential derivatives as well as the radial derivatives, where $\small{{\omega}_p(t,f)}$ denotes the $\small{L^p}$ modulus of continuity defined in terms of the unitary transformations of $\small{\mathbb{C}^n}$.
Keywords
mean Lipschitz condition;Besov space;mean modulus of continuity;
Language
English
Cited by
1.
Zygmund Type Mean Lipschitz Spaces on the Unit Ball of ℂ n, Potential Analysis, 2014, 41, 2, 543
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