This article is cited in 3 papers

Some properties of embeddings of rearrangement invariant spaces

S. V. Astashkin^a, E. M. Semenov<sup>b

a</sup> Samara National Research University, Samara, Russia
^b Voronezh State University, Voronezh, Russia

Abstract: Let $E$ and $F$ be rearrangement invariant spaces on $[0,1]$, and let $E\subset F$. 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.
Bibliography: 23 titles.

Keywords: strict embedding, rearrangement invariant (symmetric) space, Lorentz space, Marcinkiewicz space, (disjointly) strictly singular embedding.

UDC: 517.982.27

MSC: 46E30

Received: 12.04.2018 and 06.12.2018

DOI: 10.4213/sm9124

 English version: Sbornik: Mathematics, 2019, 210:10, 1361–1379

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