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Compactness criteria for spaces of measurable functions


Author: Yu. Brudnyi
Original publication: Algebra i Analiz, tom 26 (2014), nomer 1.
Journal: St. Petersburg Math. J. 26 (2015), 49-68
MSC (2010): Primary 46E30
DOI: https://doi.org/10.1090/S1061-0022-2014-01330-1
Published electronically: November 21, 2014
MathSciNet review: 3234813
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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$).


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Additional Information

Yu. Brudnyi
Affiliation: Department of Mathematics, Technion, 32000, Haifa, Israel
Email: ybrudnyi@math.technion.ac.il

DOI: https://doi.org/10.1090/S1061-0022-2014-01330-1
Keywords: Compactness, translation invariant $F$- and $B$-lattices, Orlicz classes, Marcinkiewicz--Lorentz quasi-Banach spaces
Received by editor(s): July 18, 2012
Published electronically: November 21, 2014
Article copyright: © Copyright 2014 American Mathematical Society