The infimum of small subharmonic functions

Author:
P. C. Fenton

Journal:
Proc. Amer. Math. Soc. **78** (1980), 43-47

MSC:
Primary 31A05

DOI:
https://doi.org/10.1090/S0002-9939-1980-0548081-6

MathSciNet review:
548081

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Abstract | References | Similar Articles | Additional Information

Abstract: Suppose that *u* is subharmonic in the plane and that, for some . It is shown that, given ,

*r*outside an exceptional set

*E*, where

**[1]**P. D. Barry,*The minimum modulus of small integral and subharmonic functions*, Proc. London Math. Soc.**12**(1962), 445-495. MR**0139741 (25:3172)****[2]**-,*On a theorem of Kjellberg*, Quart. J. Math. Oxford Ser. (2)**15**(1964), 179-191. MR**0164050 (29:1349)****[3]**W. K. Hayman,*The minimum modulus of large integral functions*, Proc. London Math. Soc.**2**(1952), 469-512. MR**0056083 (15:22f)****[4]**Bo Kjellberg,*On the minimum modulus of entire functions of lower order less than one*, Math. Scand.**8**(1960), 189-197. MR**0125967 (23:A3264)**

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DOI:
https://doi.org/10.1090/S0002-9939-1980-0548081-6

Article copyright:
© Copyright 1980
American Mathematical Society