ISSN:
1572-929X
Keywords:
31B05
;
Separately subharmonic
;
integrability condition
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Letu be a function on ℝ m ×ℝ n , wherem⩾2 andn⩾2, such thatu(x, .) is subharmonic on ℝ n for each fixedx in ℝ m andu(.,y) is subharmonic on ℝ m for each fixedy in ℝ n . We give a local integrability condition which ensures the subharmonicity ofu on ℝ m ×ℝ n , and we show that this condition is close to being sharp. In particular, the local integrability of (log+ u +) m+n−2+α is enough to secure the subharmonicity ofu if α〉0, but not if α〈0.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01048509
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