CONICET | Buscador de Institutos y Recursos Humanos

Let T be a positive linear operator with positive inverse. We consider in this paper the ergodic Cesàro-$alpha$ averages A_{n,alpha}f, 0<alpha⩽1, and the ergodic Cesàro-alpha maximal operator associated to T. For Lebesgue spaces Lp(ν), it is known that the good range for the convergence of the Cesàro-α averages and the boundedness of the maximal operator is 1/ alpha<p<infty. In this paper we study the convergence of A_{n_k,alpha}f, where {n_k} is a lacunary sequence, and the boundedness of its associated ergodic maximal operator. We get positive results in the range 1leq p leq 1/(1-alpha). We use transference arguments which leads to us to study in depth weighted inequalities of the lacunary Cesàro-alpha maximal operator in the setting of the integers and in the setting of the real line.