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 Mat. Sb., 2019, Volume 210, Number 10, Pages 17–36 (Mi msb9124)

Some properties of embeddings of rearrangement invariant spaces

S. V. Astashkina, E. M. Semenovb

a 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.

 Funding Agency Grant Number Ministry of Science and Higher Education of the Russian Federation 1.470.2016/1.4 Russian Foundation for Basic Research 17-01-00138-à18-01-00414-à The work of S. V. Astashkin was carried out in the framework of the implementation of a State Assignment of the Ministry of Education and Science of the Russian Federation (project no. 1.470.2016/1.4) and was also supported by the Russian Foundation for Basic Research (grant no. 17-01-00138-a). The work of E. M. Semenov was supported by the Russian Foundation for Basic Research (grant nos. 17-01-00138-a and 18-01-00414-a).

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DOI: https://doi.org/10.4213/sm9124

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

Bibliographic databases:

UDC: 517.982.27
MSC: 46E30

Citation: S. V. Astashkin, E. M. Semenov, “Some properties of embeddings of rearrangement invariant spaces”, Mat. Sb., 210:10 (2019), 17–36; Sb. Math., 210:10 (2019), 1361–1379

Citation in format AMSBIB
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