Functions of vanishing mean oscillation

Sarason, Donald

doi:10.1090/S0002-9947-1975-0377518-3

Functions of vanishing mean oscillation

Author: Donald Sarason
Journal: Trans. Amer. Math. Soc. 207 (1975), 391-405
MSC: Primary 46J10; Secondary 30A78, 42A40, 60G10
DOI: https://doi.org/10.1090/S0002-9947-1975-0377518-3
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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