The structure of subspaces in Orlicz spaces between L¹ and L²

2022/08/15 by Astashkin, S. V.
#46A45 #46B03 #46B09 #46E30 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2208.07215

Abstract

A subspace H of a rearrangement invariant space X on [0,1] is strongly embedded in X if, in H, convergence in X-norm is equivalent to convergence in measure. We obtain necessary and sufficient conditions on an Orlicz function M, under which the unit ball of an arbitrary strongly embedded subspace in the Orlicz space L_M has equi-absolutely continuous norms in L_M.

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