ABOUT THE RELATIONSHIP BETWEEN GRAND AND SMALL LEBESQUE SPACES WITH CLASSIC SYMMETRICAL SPACES
Berezhnoi E.I.
April 2025Springer
Journal of Mathematical Sciences (United States)
2025#289Issue 6889 - 904 pp.
Based on the study of geometric properties of grand Lebesque space, we give an exact description of the mutual embeddings of grand Lebesgue spaces Lα0→(ζ) and classical Orlicz Lorentz and Marcinkiewicz spaces. It turns out that the grand Lebesgue space Lα0→(ζ) for α0∈(0,1) cannot be described as an Orlicz, Lorentz, and Marcinkiewicz space. We also show that the grand Lebesgue space Lα0→(ζ) for α0∈[0,1) is not reflexive. Using duality, we give similar results for small Lebesgue spaces Lα1←(ξ).
Banach ideal space , Grand Lebesque spaces , Reflexivity , Small Lebesque spaces , Symmetrical spaces
Text of the article Перейти на текст статьи
Department of Mathematics, Yaroslavl State University, 14, Sovetskaya St., Yaroslavl, 150000, Russian Federation
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Regional Mathematical Center of Southern Federal University, 105/42 Bolshaya Sadovaya, Rostov-on-Don, 344090, Russian Federation
Department of Mathematics
Institute of Mathematics and Mathematical Modeling
Regional Mathematical Center of Southern Federal University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026