PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 55(69), pp. 1822 (1994) 

On subharmonic behaviour and oscillation of functions on balls in $R_n$Miroslav Pavlovi\'cMatematicki fakultet, Beograd, YugoslaviaAbstract: 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 submeanvalue property. Keywords: harmonic functions, submeanvalue property, oscillation Classification (MSC2000): 31B05 Full text of the article:
Electronic fulltext finalized on: 1 Nov 2001. This page was last modified: 16 Nov 2001.
© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
