Tchebyshev's characteristic of rearrangement invariant space
Functional Analysis
2012-08-14 v1
Abstract
We introduce and investigate in this short article a new characteristic of rearrangement invariant (r.i.) (symmetric) space, namely so-called Tchebychev's characteristic. We reveal an important class of the r.i. spaces - so called regular r. i. spaces and show that the majority of known r.i. spaces: Lebesgue-Riesz, Grand Lebesgue Spaces, Orlicz, Lorentz and Marcinkiewicz r.i. spaces are regular. But we construct after several examples of r.i. spaces without the regular property.
Keywords
Cite
@article{arxiv.1208.2393,
title = {Tchebyshev's characteristic of rearrangement invariant space},
author = {E. Ostrovsky and L. Sirota},
journal= {arXiv preprint arXiv:1208.2393},
year = {2012}
}