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arXiv · 1208.2393

Tchebyshev's characteristic of rearrangement invariant space

E. Ostrovsky·L. Sirota
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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.

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E. Ostrovsky, L. Sirota. 2012-08-12. Tchebyshev's characteristic of rearrangement invariant space. https://arxiv.org/abs/1208.2393

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