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

Korenblum, Boris

doi:10.1090/S0002-9947-1985-0792810-2

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

Trans. Amer. Math. Soc. 290 (1985), 527-553

DOI: https://doi.org/10.1090/S0002-9947-1985-0792810-2

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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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