Tchebyshev's characteristic of rearrangement invariant space
arXiv:1208.2393
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.
References in corpus (6)
- Nikol'skii-type inequalities for rearrangement invariant spaces
- Monte-Carlo method for multiple parametric integrals calculation and solving of linear integral Fredholm equations of a second kind, with confidence regions in uniform norm
- Integral Operators in Bilateral Grand Lebesgue Spaces
- Non-Improved Uniform Tail Estimates for Normed Sums of Independent Random Variables with Heavy Tails, with applications
- Adaptive Optimal Nonparametric Regression and Density Estimation Based on Fourier-Legendre Expansion
- Tail estimates for martingale under "LLN" norming sequence