Israel Journal of Mathematics

, Volume 54, Issue 3, pp 366–380 | Cite as

On subharmonic functions dominated by certain functions

  • H. Yoshida


Given two kinds of functionsf(X) andh(y) defined on them-dimensional Euclidean spaceR m (m≧1) and the set of positive real numbers respectively, we give an estimation of growth of subharmonic functionsu(P) defined onR m+n (n≧1) such that
$$u(P) \leqq f\left( X \right)h\left( {\left\| Y \right\|} \right)$$
for anyP=(X, Y),XR m, Y ∈R n, where ‖Y ‖ denotes the usual norm ofY. Using an obtained result, we give a sharpened form of an ordinary Phragmén-Lindelöf theorem with respect to the generalized cylinderD ×R n, with a bounded domainD inR m.


Positive Real Number Subharmonic Function Regular Domain Sharpened Form Chiba City 
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Copyright information

© Hebrew University 1986

Authors and Affiliations

  • H. Yoshida
    • 1
  1. 1.Department of Mathematics, Faculty of SciencesChiba UniversityChiba CityJapan

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