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Algebra i Analiz, 2014, Volume 26, Issue 1, Pages 68–93 (Mi aa1369)  
This article is cited in 5 scientific papers (total in 5 papers)

Research Papers

Compactness criteria for spaces of measurable functions

Yu. Brudnyi

Department of Mathematics, Technion, 32000, Haifa, Israel
Full-text PDF (350 kB) Citations (5)
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Abstract: 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 $p<1$).
Keywords: compactness, translation invariant $F$- and $B$-lattices, Orlicz classes, Marcinkiewicz–Lorentz quasi-Banach spaces.
Received: 18.07.2012
English version:
St. Petersburg Mathematical Journal, 2015, Volume 26, Issue 1, Pages 49–68
DOI: https://doi.org/10.1090/S1061-0022-2014-01330-1
Bibliographic databases:
Document Type: Article
Language: English
Citation: Yu. Brudnyi, “Compactness criteria for spaces of measurable functions”, Algebra i Analiz, 26:1 (2014), 68–93; St. Petersburg Math. J., 26:1 (2015), 49–68
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/aa1369
  • https://www.mathnet.ru/eng/aa/v26/i1/p68
    • This publication is cited in the following 5 articles:
    1. J. Huang, Y. Nessipbayev, F. Sukochev, D. Zanin, “Compactness criteria in quasi-Banach symmetric operator spaces associated with a non-commutative torus”, Journal of Functional Analysis, 2025, 110946  crossref
    2. 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  crossref
    3. 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  crossref
    4. Nguyen Anh Dao, “Hardy Factorization in Terms of Fractional Commutators in Lorentz Spaces”, Front. Math. China, 2021  crossref  isi
    5. H. Hanche-Olsen, H. Holden, E. Malinnikova, “An improvement of the Kolmogorov-Riesz compactness theorem”, Expo. Math., 37:1 (2019), 84–91  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и анализ St. Petersburg Mathematical Journal
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    Abstract page:380
    Full-text PDF :142
    References:70
    First page:19
     
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