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infimum

Proceedings of the Edinburgh Mathematical Society (1)

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Supremum and infimum of subharmonic functions of order between 1 and 2
Part of
- Two-dimensional theory
P. C. Fenton
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 54 / Issue 3 / October 2011

Published online by Cambridge University Press:

08 April 2011, pp. 685-693
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For functions u, subharmonic in the plane, let
and let N(r,u) be the integrated counting function. Suppose that is a non-negative non-decreasing convex function of log r for which for all small r and , where 1 < ρ < 2, and define
A sharp upper bound is obtained for and a sharp lower bound is obtained for .