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 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 
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     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 },
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     number = {69},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1994_N_S_55_69_a2/}
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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/