Moustafa Damlakhi
Abstract:
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 email: damlakhi@ksu.edu.sa |
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