Let {cj} be a null sequence of bounded variation. We give appreciate smoothness and growth conditions on {cj} to obtain the pointwise convergence as well as Lr-convergence of Laguerre series cj𝔏ja. Then, we prove a Hardy-Littlewood type inequality 0|f(t)|rdtCj=0|cj|rj¯1r/2 for certain r1, where f is the limit function of cj𝔏ja. Moreover, we show that if f(x)cj𝔏ja is in Lr, r1, we have the converse Hardy-Littlewood type inequality j=0|cj|rj¯βC0|f(t)|rdt for r1 and β<r/2.