Separately harmonic and subharmonic functions |
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| Authors: | S?awomir Ko?odziej Johan Thorbiörnson |
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| Institution: | (1) Department of Mathematics, Jagiellonian University, ul. Reymonta 4, 30-059 Krakow, Poland;(2) Department of Mathematics, Midsweden University, S-851 70 Sundsvall, Sweden |
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| Abstract: | Let u(x, y) be defined in B
1×B
2 where B
1 
m
and B
2
n
, and assume that u(x, ·) harmonic for every fixed x and u(·, y) is subharmonic for every fixed y. We show that if u(·, y) is, in addition, C
2 for each y then u is subharmonic in B
1×B
2 in both variables jointly. |
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| Keywords: | 31B05 |
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