Weak and strong type inequalities for Orlicz spaces

Abstract

We revisit the generalisation of Calderon’s Transfer Principle as espoused in [7]. This principle is used to generate weak type maximal  inequalities for ergodic operators in the setting of σ-compact locally compact Hausdorff groups acting measure-preservingly on σ-finite  measure spaces. In particular we develop a much more robust protocol for transferring weak and strong type inequalities from Orlicz spaces in the group setting to Orlicz spaces in the measure space setting. This is an important addition to the protocol developed in [7],  which to date has only yielded weak type inequalities. The current approach also places fewer restrictions on the underlying Young  functions describing the Orlicz spaces involved.