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A critical growth rate for harmonic and subharmonic functions in the open ball in \({\mathbb{R}}^ n\). (English) Zbl 0657.35005

This paper presents certain technique of investigation of properties of harmonic or subharmonic functions h in the open unit ball in \({\mathbb{R}}^ n\) (n\(\geq 2)\) that have restricted growth in the sense that \(\sup \{h(x)| | x| =r\}\leq Ck(r)\) \((C=const)\) for some fixed function k.
We assume that k is defined in [0,1) and continuous, positive, nondecreasing and unbounded therein.

MSC:

35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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