2012/08/12 by E. Ostrovsky, Ostrovsky, E., L. Sirota +1
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #math.FA
paper · pdf · doi:10.48550/arxiv.1208.2393
arxiv created 2012/08/12 · openalex publication_date 2012/08/12 · arxiv updated 2012/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.