English

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}
}