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 $i\in\{0,1,2\}$ , $10$ , 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.
Publié le : 2007-04-14
Classification:
weighted integrals,
harmonic functions,
area inequality,
integral mean,
31B05
@article{1191247600,
author = {STEVI\'C, Stevo},
title = {Area type inequalities and integral means of harmonic functions on the unit ball},
journal = {J. Math. Soc. Japan},
volume = {59},
number = {1},
year = {2007},
pages = { 583-601},
language = {en},
url = {http://dml.mathdoc.fr/item/1191247600}
}
STEVIĆ, Stevo. Area type inequalities and integral means of harmonic functions on the unit ball. J. Math. Soc. Japan, Tome 59 (2007) no. 1, pp. 583-601. http://gdmltest.u-ga.fr/item/1191247600/