Remote Access Transactions of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9947-1972-0294671-8
MathSciNet review: 0294671
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 31A05

Retrieve articles in all journals with MSC: 31A05


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0294671-8
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