Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Inequalities for the integral means of holomorphic functions and their derivatives in the unit ball of $ \bold C\sp n$


Author: Ji Huai Shi
Journal: Trans. Amer. Math. Soc. 328 (1991), 619-637
MSC: Primary 32A10; Secondary 31C10, 32F05
DOI: https://doi.org/10.1090/S0002-9947-1991-1016807-5
MathSciNet review: 1016807
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, the following two inequalities are proved:

$\displaystyle \int_0^1 {{(1 - r)}^{a\vert\alpha\vert + b}}M_p^a(r,D^{\alpha} f)... ...alpha \vert = m} \int_0^1 {(1 - r)}^{am + b}M_p^a(r,D^{\alpha }f)\,dr \right\} $

where $ \alpha = ({\alpha _1}, \ldots,{\alpha _n})$ is multi-index, $ 0 < p < \infty,0 < a < \infty $ and $ - 1 < b < \infty $. These are a generalization of some classical results of Hardy and Littlewood. Using these two inequalities, we generalize a theorem in $ [9]$. The methods used in the proof of Theorem 1 lead us to obtain Theorem 7, which enables us to generalize some theorems about the pluriharmonic conjugates in $ [8]$ and $ [2]$.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 32A10, 31C10, 32F05

Retrieve articles in all journals with MSC: 32A10, 31C10, 32F05


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1991-1016807-5
Article copyright: © Copyright 1991 American Mathematical Society