Holomorphic mean Lipschitz functions on the unit ball of $\mathbb C^n$

Ern Gun Kwon; Hong Rae Cho; Hyungwoon Koo

doi:10.4134/JKMS.2013.50.1.189

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2013; 50(1): 189-202

Printed January 1, 2013

https://doi.org/10.4134/JKMS.2013.50.1.189

Holomorphic mean Lipschitz functions on the unit ball of $\mathbb C^n$

Ern Gun Kwon, Hong Rae Cho, and Hyungwoon Koo

Andong National University, Pusan National University, Korea University

Abstract

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Abstract

On the unit ball of $\mathbb C^n$, the space of those holomorphic functions satisfying the mean Lipschitz condition \begin{align*} \int_0^1 \omega_p(t, f)^q \frac{dt}{t^{1+\alpha q}} <\infty\end{align*} is characterized by integral growth conditions of the tangential derivatives as well as the radial derivatives, where $\omega_p(t, f)$ denotes the $L^p$ modulus of continuity defined in terms of the unitary transformations of $\mathbb{C}^n$.

Keywords: mean Lipschitz condition, Besov space, mean modulus of continuity

MSC numbers: 32A30, 30H25