On Young's criteria for the convergence of Fourier series and their conjugates
W. L. C. Sargent · Mathematical Proceedings of the Cambridge Philosophical Society · 1929
1. Young's criterion for the convergence of a Fourier series may be stated in the following form: The integral tends to zero as ω → ∞ whenever (A) ø(t) is absolutely integrable in (0, a), (B) ø(t) → 0 in mean as t → 0, (C) tø(t) is of bounded variation to the immediate right of t = 0 and, as t → 0,