Let (X,F,ν) be a σ-finite measure space. Associated with k Lamperti operators on Lp(ν), T1,…,Tk, nˉ=(n1,…,nk)∈Nk and αˉ=(α1,…,αk) with 01/α∗ where α∗=min1≤j≤kαj. In the limit case p=1/α∗, we prove that the averages Rnˉ,αˉf converge almost everywhere on X for all f in the Orlicz–Lorentz space Λ(1/α∗,φm−1) with φm(t)=t(1+log+t)m. To obtain the result in the limit case we need to study inequalities for the composition of operators Ti that are of restricted weak type (pi,pi). As another application of these inequalities we also study the strong Cesàro-αˉ continuity of functions.

Fil: Bernardis, Ana Lucia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina

Fil: Crescimbeni, Raquel Liliana. Universidad Nacional del Comahue; Argentina

Fil: Ferrari Freire, Cecilia. Universidad Nacional del Comahue; Argentina