Area type inequalities and integral means of harmonic functions on the unit ball
Stevo STEVIĆ
Source: J. Math. Soc. Japan Volume 59, Number 2 (2007), 583-601.
Abstract
In this paper we investigate the relationship among the following integrals $$\int_B|u(x)|^{p-i} |\nabla u(x)|^i(1-|x|)^\alpha dV(x),$$where $i\in\{0,1,2\}$, $1<p<\infty$, $\alpha>0$, and where $u$ is an arbitrary harmonic function on the unit ball $B\subset\bm{R}^n$. Growth of the integral means of harmonic functions is also compared to the integral means of their gradient.
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Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1191247600
Digital Object Identifier: doi:10.2969/jmsj/05920583
Mathematical Reviews number (MathSciNet):
MR2326178
Journal of the Mathematical Society of Japan
