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On subharmonic functions dominated by certain functions

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Abstract

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),X ∈R 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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Chiba University, Chiba City, Japan

    H. Yoshida

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  1. H. Yoshida
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Yoshida, H. On subharmonic functions dominated by certain functions. Israel J. Math. 54, 366–380 (1986). https://doi.org/10.1007/BF02764964

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  • DOI: https://doi.org/10.1007/BF02764964

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