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 l(n)a(x) = (n!/GAMMA(n + a + 1))1/2e(-x/2)L(n)a(x), n = 0, 1, 2,..., in L2(R+, x(a)dx), a greater-than-or-equal-to 0. We prove that the Cesaro means of order delta > a+2/3 of any function f is-an-element-of L(p)(x(a)dx), 1 less-than-or-equal-to p less-than-or-equal-to infinity, converge to f a.e. The main tool we use is a Hardy-Littlewood type maximal operator associated with a generalized Euclidean convolution.