Transfer principles and ergodic theory in Orlicz spaces

Abstract

We extend to Orlicz spaces with weight a transfer principle of R. Coifman, G.Weiss, concerning L_p-inequalities on some convolution operators. We also extend to Orlicz spaces the Birkhoff's pointwise ergodic theorem, and L_p-inequalities on some maximal operators using a transfer argument which follows Wiener and Calderon's ideas. We get a new characterization of the so called Dini-condition.