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

Title & Authors
INEQUALITIES FOR THE INTEGRAL MEANS OF HOLOMORPHIC FUNCTIONS IN THE STRONGLY PSEUDOCONVEX DOMAIN
CHO, HONG-RAE; LEE, JIN-KEE;

Abstract
We obtain the following two inequalities on a strongly pseudoconvex domain $\small{\Omega\;in\;\mathbb{C}^n\;:\;for\;f\;{\in}\;O(\Omega)}$ $\small{\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 $\small{\mathbb{C}^n}$. These are generalizations of some classical results of Hardy and Littlewood.
Keywords
strongly pseudo convex domain;integral means;Levi polynomial;
Language
English
Cited by
1.
On Traces in Some Analytic Spaces in Bounded Strictly Pseudoconvex Domains, Journal of Function Spaces, 2015, 2015, 1
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