Some properties of embeddings of rearrangement invariant spaces

被引：2

作者：

Astashkin, S., V ^{[1
]}

Semenov, E. M. ^{[2
]}

机构：

[1] Samara Natl Res Univ, Samara, Russia

[2] Voronezh State Univ, Voronezh, Russia

来源：

SBORNIK MATHEMATICS | 2019年 / 210卷 / 10期

基金：

俄罗斯基础研究基金会;

关键词：

strict embedding; rearrangement invariant (symmetric) space; Lorentz space; Marcinkiewicz space; (disjointly) strictly singular embedding; INTERPOLATION;

D O I：

10.1070/SM9124

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let E and F be rearrangement invariant spaces on [0, 1], and let E subset of F. This embedding is said to be strict if the functions in the unit ball of the space E have absolutely equicontinuous norms in F. For the main classes of rearrangement invariant spaces necessary and sufficient conditions are obtained for an embedding to be strict, and also the relationships this concept has with other properties of embeddings are studied, especially the property of disjoint strict singularity. In the final part of the paper, a characterization of the property of strict embedding in terms of interpolation spaces is obtained.

引用

页码：1361 / 1379

页数：19

共 23 条

[1]

Asekritova I. U., 1980, ISSLED TEOR FUNKTS M, P3

[2] Strict Embeddings of Rearrangement Invariant Spaces [J].