A Banach rearrangement norm characterization for tail behavior of measurable functions (random variables)

Abstract

We construct a Banach rearrangement invariant norm on the measurable space for which the finiteness of this norm for measurable function (random variable) is equivalent to suitable tail (heavy tail and light tail) behavior. We investigate also a conjugate to offered spaces and obtain some embedding theorems. Possible applications: Functional Analysis (for instance, interpolation of operators), Integral Equations, Probability Theory and Statistics (tail estimations for random variables).

Cited by in corpus (4)

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• Individual lower bound for Calderon's generalized Lorentz norm estimates
• Hardy's operator and normability of generalized Lorentz-Marcinkiewicz spaces, with sharp or weakly sharp constant estimation
• Quasi Grand Lebesgue Spaces