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Subharmonic Functions of Order Less than One
Authors:Email author" target="_blank">Rapha?le?SupperEmail author
Institution:(1) UFR de Mathématique et Informatique, URA CNRS 001, Université Louis Pasteur, 7 rue René Descartes, F-67 084 Strasbourg Cedex, France
Abstract:We study suhharmonic functions u in RN (Nge3) of order at most one, growing so slowly that $\liminf_{r\rightarrow +\infty}\frac{M(u,r)}{\varphi (r)}\leqslant 1$ for some function phgr, with M(u,r)=maxthinsp|x|=ru(x). We obtain minorisations for negative values of u(x) and estimations of the difference u(y)–u(x) for x and y on a same sphere. Mathematics Subject Classifications (2000) 31B05, 31B10; secondary: 26A12, 26D15.
Keywords:subharmonic functions  Riesz measure  order of growth
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