Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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HOLOMORPHIC MEAN LIPSCHITZ FUNCTIONS ON THE UNIT BALL OF ℂn

  • Kwon, Ern Gun (Department of Mathematics Education Andong National University) ;
  • Cho, Hong Rae (Department of Mathematics Pusan National University) ;
  • Koo, Hyungwoon (Department of Mathematics Korea University)
  • Received : 2012.02.21
  • Published : 2013.01.01
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Abstract

On the unit ball of $\mathbb{C}^n$, the space of those holomorphic functions satisfying the mean Lipschitz condition $${\int}_0^1\;{\omega}_p(t,f)^q\frac{dt}{t^1+{\alpha}q}\;<\;{\infty}$$ 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 $\mathbb{C}^n$.

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Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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Cited by

  1. Zygmund Type Mean Lipschitz Spaces on the Unit Ball of ℂ n vol.41, pp.2, 2014, https://doi.org/10.1007/s11118-013-9382-5