A Characterization of Some Classes of Harmonic Functions期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

首页 | 本学科首页

官方微博 | 高级检索

按检索

A Characterization of Some Classes of Harmonic Functions

Authors:

Stevo Stević

Institution:

(1) Mathematical Institute of the Serbian Academy of Science, Knez Mihailova 35/I, 11000 Beograd, Serbia

Abstract:

In this paper we investigate harmonic Hardy-Orlicz ${\mathcal{H}}_\varphi (B)$ and Bergman-Orlicz b _φ,α(B) spaces, using an identity of Hardy-Stein type. We also extend the notion of the Lusin property by introducing (φ, α)-Lusin property with respect to a Stoltz domain. The main result in the paper is as follows: Let $\alpha \in -1,\infty), \varphi$ be a nonnegative increasing convex function twice differentiable on (0, ∞), and u a harmonic function on the unit ball B in ${\mathbb{R}}^n$ . Then the following statements are equivalent:

(a)	$u \in b{\varphi,\alpha}(\it B), \rm{if} \alpha \in (-1, \infty).\,\, u \in {\mathcal{H}_\varphi}(\it B)\, \rm{if}\, \alpha = -1$ .
(b)	$\int_B \varphi^{\prime\prime}(\|u(x)\|)\|\nabla u(x)\|^2(1 - \|x\|)^{\alpha + 2} dV(x) < + \infty$ .
(c)	u has (φ, α)-Lusin property with respect to a Stoltz domain with half-angle β, for any $\beta \in (0, \pi/2 )$ .
(d)	u has (φ, α)-Lusin property with respect to a Stoltz domain with half-angle β, for some $\beta \in (0, \pi/2 )$ .

Keywords:

Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 31B05

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏