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

E. Ostrovsky; L. Sirota

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arXiv · 1211.6415

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

E. Ostrovsky·L. Sirota

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Abstract

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

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E. Ostrovsky, L. Sirota. 2012-11-27. Hardy's operator and normability of generalized Lorentz-Marcinkiewicz spaces, with sharp or weakly sharp constant estimation. https://arxiv.org/abs/1211.6415

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