Authors: Stević, Stevo 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: A characterization of some classes of harmonic functions
Journal: Mediterranean Journal of Mathematics
Volume: 5
Issue: 1
First page: 61
Last page: 76
Issue Date: 1-Apr-2008
Rank: M23
ISSN: 1660-5446
DOI: 10.1007/s00009-008-0136-3
Abstract: 
In this paper we investigate harmonic Hardy-Orlicz Hφ(B) and Bergman-Orlicz bφ,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 α ∈ [-1,∞), φ be a nonnegative increasing convex function twice differentiable on (0, ∞), and u a harmonic function on the unit ball B in ℝn. Then the following statements are equivalent: (a) u ∈ bφ,α(B), if α ∈ (-1,∈). u ∈ Hφ(B) if α = -1. (b) ∫B φ″ (|u(x)|)|∇ u(x)|2(1 - |x|)α + 2 dV(x) < + ∞. (c) u has (φ, α)-Lusin property with respect to a Stoltz domain with half-angle β, for any β ∈ (0, π/2 ). (d) u has (φ, α)-Lusin property with respect to a Stoltz domain with half-angle β, for some β ∈ (0, π/2).
Keywords: Bergman-Orlicz space | Hardy-Orlicz space | Harmonic functions | Lusin property
Publisher: Springer Link

Show full item record

Page view(s)

12
checked on Sep 15, 2022

Google ScholarTM

Check

Altmetric

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.