We prove that if u is an -subharmonic function defined outside a compact set in , it is bounded above near infinity, in particular, if the subharmonic function u is in , , then u is non-positive. Some of the consequences of this property are obtained. We discuss the properties of subharmonic functions defined outside a compact set in if they are also functions.
Submitted August 8, 2016. Published December 20, 2016.
Math Subject Classifications: 31B05, 30D55.
Key Words: L^p-subharmonic functions; harmonic Hardy class
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| Moustafa Damlakhi |
Department of Mathematics
College of Science, King Saud University
P.O. Box 2455, Riyadh 11451, Saudi Arabia
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