Analysis Mathematica

, Volume 11, Issue 3, pp 257–282

Аппроксимация субга рмонических функций

Authors

  • Р. С. Юлмухаметов
    • ОТДЕЛ Ф ИЗИКИ И МАТЕМАТИКИБАШКИРСКИЙ ФИЛИАЛ АКАДЕМИИ НАУК
Article

DOI: 10.1007/BF01907421

Cite this article as:
Юлмухаметов, Р.С. Analysis Mathematica (1985) 11: 257. doi:10.1007/BF01907421

Approximation of subharmonic functions

Abstract

The following statement is proved. Letu be a subharmonic function in the regionΩ andμu the associated measure. Then there exists a functionf holomorphic inΩ and such that ifμf is the associated measure of the function in ¦f¦, then ¦u(z)−ln¦f(z)¦ ≦A¦ln s¦+B¦ln diamΩ¦+β s(¦lns¦+1)+C. hold at every point z for which the setsD(z, t)={w: ¦w−z¦<t},t∈(0,s) lie inΩ and satisfyμ(D(z, t))≦βt both forμ=μu and forμ=μf. In the case whereΩ is an unbounded region, In diamΩ should be replaced by ln ¦z¦. The constantsА, В, С do not depend onΩ andu.

Copyright information

© Akadémiai Kiadó 1985