Absolute Abel Summability and Capacity

G. V. Welland
1979 Proceedings of the American Mathematical Society  
Precise limits on the size of exceptional sets for which functions in the Lebesgue class, ££, can fail to be absolutely Abel summable are given in terms of Bessel capacity. wherega(ft,/) = ¡ff(y)ga(x -y) dp(x) dy. We say a function / belongs to the Lebesgue class ££ if / can be written as /o * ga for some/0 in L" = Lp(Qk).
doi:10.2307/2042643 fatcat:m6paenh3s5dzrknfpyjzhdkfza