Authors: Stević, Stevo 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Area type inequalities and integral means of harmonic functions on the unit ball
Journal: Journal of the Mathematical Society of Japan
Volume: 59
Issue: 2
First page: 583
Last page: 601
Issue Date: 1-Apr-2007
Rank: M22
ISSN: 0025-5645
DOI: 10.2969/jmsj/05920583
Abstract: 
In this paper we investigate the relationship among the following integrals ∫B|u(x)|p-i|∇u(x)|i(1 - |x| ) α, where i ∈ {0,1,2}, 1 < p < ∞, α >0, and where u is an arbitrary harmonic function on the unit ball B ⊂ Rn. Growth of the integral means of harmonic functions is also compared to the integral means of their gradient.
Keywords: Area inequality | Harmonic functions | Integral mean | Weighted integrals
Publisher: Mathematical Society of Japan

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