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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Functions of vanishing mean oscillation


Author: Donald Sarason
Journal: Trans. Amer. Math. Soc. 207 (1975), 391-405
MSC: Primary 46J10; Secondary 30A78, 42A40, 60G10
MathSciNet review: 0377518
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Abstract: A function of bounded mean oscillation is said to have vanishing mean oscillation if, roughly speaking, its mean oscillation is locally small, in a uniform sense. In the present paper the class of functions of vanishing mean oscillation is characterized in several ways. This class is then applied to answer two questions in analysis, one involving stationary stochastic processes satisfying the strong mixing condition, the other involving the algebra $ {H^\infty } + C$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0377518-3
PII: S 0002-9947(1975)0377518-3
Article copyright: © Copyright 1975 American Mathematical Society