Transfer principles and ergodic theory in Orlicz spaces

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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.