Absolute Abel summability and capacity
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- by G. V. Welland
- Proc. Amer. Math. Soc. 77 (1979), 223-228
- DOI: https://doi.org/10.1090/S0002-9939-1979-0542089-4
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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
- A. Beurling, Sur les ensembles exceptionels, Acta Math. 72 (1940), 1-13.
- 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
Bibliographic Information
- © Copyright 1979 American Mathematical Society
- 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