Absolute Abel summability and capacity

Welland, G. V.

doi:10.1090/S0002-9939-1979-0542089-4

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Absolute Abel summability and capacity
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by G. V. Welland PDF

Proc. Amer. Math. Soc. 77 (1979), 223-228 Request permission

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

Sur les ensembles exceptionels

Gary E. Lippman and Victor L. Shapiro, Capacity and absolute Abel summability of multiple Fourier series, J. Approximation Theory 10 (1974), 313–323. MR 365018, DOI 10.1016/0021-9045(74)90103-8
Norman G. Meyers, A theory of capacities for potentials of functions in Lebesgue classes, Math. Scand. 26 (1970), 255–292 (1971). MR 277741, DOI 10.7146/math.scand.a-10981