Hardy spaces for Laguerre expansions

Let L-n(a)(x) be the standard Laguerre functions of type a. We denote phi(a)(n)(x) = L-n(a)(x(2))(2x)(1/2). Let T-t f(x) =Sigma(n) e(-(n+(a+1)/2)t) < f, L-n(a)> L-n(a)(x) and T-t f(x) = Sigma(n) e(-(4n+2a+2)t) < f, phi(a)(n)>phi(a)(n)(x) be the semigroups associated with the orthonormal systems L-n(a) and phi(a)(n). We say that a function f belongs to the Hardy space H-1 associated with one of the semigroups if the corresponding maximal function belongs to L-1((0, infinity), dx). We prove special atomic decompositions of the elements of the Hardy spaces.