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We introduce a Banach rearrangement invariant (tail) quasy-norm by means ofHardy's (Cesaro) average on the (measurable) functions defined on somemeasurable space which is a slight generalization of classicalLorentz-Marcinkiewicz norm and find for it an equivalent norm expression.

Hardy's operator and normability of generalized Lorentz-Marcinkiewicz spaces, with sharp or weakly sharp constant estimation