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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