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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Some theorems on the cos $ \pi\ \lambda $ inequality

Author: John L. Lewis
Journal: Trans. Amer. Math. Soc. 167 (1972), 171-189
MSC: Primary 31A05
MathSciNet review: 0294671
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Abstract: In this paper we consider subharmonic functions $ u \leqq 1$ in the unit disk whose minimum modulus and maximum modulus satisfy a certain inequality. We show the existence of an extremal member of this class with largest maximum modulus. We then obtain an upper bound for the maximum modulus of this function in terms of the logarithmic measure of a certain set. We use this upper bound to prove theorems about subharmonic functions in the plane.

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Keywords: Subharmonic functions, harmonic functions, minimum modulus, maximum modulus, $ \cos \pi \lambda $ inequality, growth of the maximum modulus, order, lower order, logarithmic measure, upper logarithmic density, lower logarithmic density
Article copyright: © Copyright 1972 American Mathematical Society

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