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 },
     publisher = {mathdoc},
     volume = {_N_S_55},
     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/