Almost everywhere convergence of Fourier integrals

摘要

Let f ∈ L~p(R~n), 1 ≤ p ≤ ∞. The Fourier transform F of f is known as the tempered distribution on R~n satisfying F(φ) = ∫_(R~n) f(x)φ(x)dx for all φ ∈ J.