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

 

On a class of Banach spaces of functions associated with the notion of entropy


Author: Boris Korenblum
Journal: Trans. Amer. Math. Soc. 290 (1985), 527-553
MSC: Primary 46E99; Secondary 30D99, 42A20
MathSciNet review: 792810
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Abstract: A class of function spaces on the circle is introduced which contain all continuous functions of bounded variation but are included in the set of all continuous functions. The corresponding dual spaces consist of certain types of generalized measures. One application of these spaces is a new convergence test for Fourier series which includes both the Dirichlet-Jordan and the Dini-Lipschitz tests.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0792810-2
PII: S 0002-9947(1985)0792810-2
Article copyright: © Copyright 1985 American Mathematical Society