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Proceedings of the American Mathematical Society

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Absolute Abel summability and capacity


Author: G. V. Welland
Journal: Proc. Amer. Math. Soc. 77 (1979), 223-228
MSC: Primary 42B05
DOI: https://doi.org/10.1090/S0002-9939-1979-0542089-4
MathSciNet review: 542089
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Abstract: Precise limits on the size of exceptional sets for which functions in the Lebesgue class, $ \mathcal{L}_\alpha ^p$, can fail to be absolutely Abel summable are given in terms of Bessel capacity.


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

  • [1] A. Beurling, Sur les ensembles exceptionels, Acta Math. 72 (1940), 1-13.
  • [2] G. E. Lippman and V. L. Shapiro, Capacity and absolute Abel summability of multiple Fourier series, J. Approximation Theory 10 (1974), 313-323. MR 0365018 (51:1271)
  • [3] N. G. Meyers, A theory of capacities for potentials of functions in Lebesgue classes, Math. Scand. 26 (1970), 255-292. MR 0277741 (43:3474)

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DOI: https://doi.org/10.1090/S0002-9939-1979-0542089-4
Article copyright: © Copyright 1979 American Mathematical Society

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