Almost everywhere convergence of Laguerre series
Volume 109 / 1994
Studia Mathematica 109 (1994), 291-301
DOI: 10.4064/sm-109-3-291-301
Abstract
Let $a ∈ ℤ^+$ and $f ∈ L^p (ℝ^+), 1 ≤ p ≤ ∞ $. Denote by $c_j$ the inner product of f and the Laguerre function $ℒ^a_j$. We prove that if ${c_j}$ satisfies $lim_{λ↓1} \overline lim_{n→∞} ∑_{n
