Geodesic
On Subharmonic Behaviour and Oscillation of Functions on Balls in Rn
Publications de l'Institut Mathématique, _N_S_55 (1994) no. 69, p. 18 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Voir la notice de l'article

We give sufficient conditions for a nonnegative function to behave like a subharmonic function. If $f$ is a $C^1$-function on a domain $D\subset R^n$ such that $|\nabla f(a)|\leq Kr^{-1}$ $\omega_f(a,r)$ ($K=$const) where $\omega_f(a,r)$ is the oscillation of $f$ on the ball $B_r(a)\subset D$, then both $|f|^p$ and $|\nabla f|^p$ ($p>0$) have a weakened sub-mean-value property.
Classification : 31B05
Keywords: harmonic functions, sub-mean-value property, oscillation 
@article{PIM_1994_N_S_55_69_a2,
     author = {Miroslav Pavlovi\'c},
     title = {On {Subharmonic} {Behaviour} and {Oscillation} of {Functions} on {Balls} in {Rn}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {18 },
     year = {1994},
     volume = {_N_S_55},
     number = {69},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1994_N_S_55_69_a2/}
}
TY  - JOUR
AU  - Miroslav Pavlović
TI  - On Subharmonic Behaviour and Oscillation of Functions on Balls in Rn
JO  - Publications de l'Institut Mathématique
PY  - 1994
SP  - 18 
VL  - _N_S_55
IS  - 69
UR  - http://geodesic.mathdoc.fr/item/PIM_1994_N_S_55_69_a2/
LA  - en
ID  - PIM_1994_N_S_55_69_a2
ER  - 
%0 Journal Article
%A Miroslav Pavlović
%T On Subharmonic Behaviour and Oscillation of Functions on Balls in Rn
%J Publications de l'Institut Mathématique
%D 1994
%P 18 
%V _N_S_55
%N 69
%U http://geodesic.mathdoc.fr/item/PIM_1994_N_S_55_69_a2/
%G en
%F PIM_1994_N_S_55_69_a2
Miroslav Pavlović. On Subharmonic Behaviour and Oscillation of Functions on Balls in Rn. Publications de l'Institut Mathématique, _N_S_55 (1994) no. 69, p. 18 . http://geodesic.mathdoc.fr/item/PIM_1994_N_S_55_69_a2/