Аннотация:
The paper contains new compactness criteria for a wide class of translation-invariant spaces of measurable functions. The results imply new compactness theorems for the families of Orlicz classes (such as $L_0(\mathbb R^d)$) and Marcinkiewicz–Lorentz spaces (including $L_{pq}$ with $p<1$).
\RBibitem{Bru14}
\by Yu.~Brudnyi
\paper Compactness criteria for spaces of measurable functions
\jour Алгебра и анализ
\yr 2014
\vol 26
\issue 1
\pages 68--93
\mathnet{http://mi.mathnet.ru/aa1369}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3234813}
\elib{https://elibrary.ru/item.asp?id=21826345}
\transl
\jour St. Petersburg Math. J.
\yr 2015
\vol 26
\issue 1
\pages 49--68
\crossref{https://doi.org/10.1090/S1061-0022-2014-01330-1}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84913580919}
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Эта публикация цитируется в следующих 4 статьяx:
Nguyen Anh Dao, Steven G. Krantz, “On the Predual of a Morrey–Lorentz Space and Its Applications to the Linear Calderón–Zygmund Operators”, Front. Math, 19:3 (2024), 385
Xiangxing Tao, Yuan Zeng, Xiao Yu, “Boundedness and Compactness for the Commutator of the ω-Type Calderón-Zygmund Operator on Lorentz Space”, Acta Math Sci, 43:4 (2023), 1587
Nguyen Anh Dao, “Hardy Factorization in Terms of Fractional Commutators in Lorentz Spaces”, Front. Math. China, 2021
H. Hanche-Olsen, H. Holden, E. Malinnikova, “An improvement of the Kolmogorov-Riesz compactness theorem”, Expo. Math., 37:1 (2019), 84–91