Almost everywhere summability of Laguerre series

We apply a construction of generalized twisted convolution to investigate almost everywhere summability of expansions with respect to the orthonormal system of functions ${\displaystyle {\ell }_n^a\left(x\right)={\left(n\frac{!}{\Gamma }(n+a+1)\right)}^{\frac{1}{2}}{e}^{-\frac{x}{2}}{L}_n^a\left(x\right)}$, n = 0,1,2,..., in ${\displaystyle L^2({ℝ}_{+},x^{a}dx)}$, a ≥ 0. We prove that the Cesàro means of order δ > a + 2/3 of any function ${\displaystyle f\in L^p\left(x^{a}dx\right)}$, 1 ≤ p ≤ ∞, converge to f a.e. The main tool we use is a Hardy-Littlewood type maximal operator associated with a generalized Euclidean convolution.