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Supremum and infimum of subharmonic functions of order between 1 and 2
Published online by Cambridge University Press: 08 April 2011
Abstract
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 .
Keywords
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 3 , October 2011 , pp. 685 - 693
- Copyright
- Copyright © Edinburgh Mathematical Society 2011