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Transactions of the American Mathematical Society

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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.

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

  • [1] A. Zygmund, Trigonometric series, Cambridge Univ. Press, Cambridge, 1959. MR 0107776 (21:6498)
  • [2] B. Korenblum, An extension of the Nevanlinna theory, Acta Math. 135 (1975), 187-219. MR 0425124 (54:13081)
  • [3] -, A Beurling-type theorem, Acta Math. 138 (1977), 265-293. MR 0447584 (56:5894)
  • [4] A. M. Garsia and S. Sawyer, On some classes of continuous functions with convergent Fourier series, J. Math. Mech. 13 (1964), 589-601. MR 0199634 (33:7777)
  • [5] D. Waterman, On convergence of Fourier series of functions of generalized bounded variation, Studia Math. 44 (1972), 107-117. MR 0310525 (46:9623)
  • [6] R. A. Fefferman, A theory of entropy in Fourier analysis, Adv. in Math. 30 (1978), 171-201. MR 520232 (81g:42022)

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Article copyright: © Copyright 1985 American Mathematical Society

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