CONVERGENCE ALMOST EVERYWHERE OF CERTAIN PARTIAL SUMS OF FOURIER INTEGRALS
Anthony Carbery, Dirk Gorges, G. Marletta, Christoph M. Thiele · Bulletin of the London Mathematical Society · 2003
Suppose that R goes to infinity through a second-order lacunary set. Let SR denote the Rth spherical partial inverse Fourier integral on Rd. Then SRf converges almost everywhere to f, provided that f satisfies ∫ ∣ f ^ ( ξ ) log ( 8 + ∣ ξ ∣ ) ∣ 2 d ξ < ∞ . 2000 Mathematics Subject Classification 42B15, 42B25, 42B08.