# INEQUALITIES FOR THE INTEGRAL MEANS OF HOLOMORPHIC FUNCTIONS IN THE STRONGLY PSEUDOCONVEX DOMAIN

CHO, HONG-RAE;LEE, JIN-KEE

• Published : 2005.04.01
• 39 6

#### Abstract

We obtain the following two inequalities on a strongly pseudoconvex domain $\Omega\;in\;\mathbb{C}^n\;:\;for\;f\;{\in}\;O(\Omega)$ $$\int_{0}^{{\delta}0}t^{a{\mid}a{\mid}+b}M_p^a(t, D^{a}f)dt\lesssim\int_{0}^{{\delta}0}t^{b}M_p^a(t,\;f)dt\;\int_{O}^{{\delta}O}t_{b}M_p^a(t,\;f)dt\lesssim\sum_{j=0}^{m}\int_{O}^{{\delta}O}t^{am+b}M_{p}^{a}$t,\;\aleph^{i}f$dt$$. In [9], Shi proved these results for the unit ball in $\mathbb{C}^n$. These are generalizations of some classical results of Hardy and Littlewood.

#### Keywords

strongly pseudo convex domain;integral means;Levi polynomial

#### References

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#### Cited by

1. On Traces in Some Analytic Spaces in Bounded Strictly Pseudoconvex Domains vol.2015, 2015, https://doi.org/10.1155/2015/265245