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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 Lp-inequalities on some convolution operators. We also extend to Orlicz spaces the Birkhoff's pointwise ergodic theorem, and Lp-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.

DOI Code: 10.1285/i15900932v25n1p167

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