Compactness criteria for spaces of measurable functions

Brudnyi, Yu.

doi:10.1090/S1061-0022-2014-01330-1

Compactness criteria for spaces of measurable functions
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by Yu. Brudnyi

St. Petersburg Math. J. 26 (2015), 49-68

DOI: https://doi.org/10.1090/S1061-0022-2014-01330-1

Published electronically: November 21, 2014

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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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