Samotij, Krzysztof A critical growth rate for harmonic and subharmonic functions in the open ball in \({\mathbb{R}}^ n\). (English) Zbl 0657.35005 Colloq. Math. 52, 145-158 (1987). 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. Cited in 1 Document MSC: 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs Keywords:harmonic; subharmonic; open unit ball; restricted growth PDFBibTeX XMLCite \textit{K. Samotij}, Colloq. Math. 52, 145--158 (1987; Zbl 0657.35005) Full Text: DOI