Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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INEQUALITIES FOR THE INTEGRAL MEANS OF HOLOMORPHIC FUNCTIONS IN THE STRONGLY PSEUDOCONVEX DOMAIN

  • CHO, HONG-RAE (Department of Mathematics Pusan National University) ;
  • LEE, JIN-KEE (Department of Mathematics Education Andong National University)
  • Published : 2005.04.01
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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.

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References

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