Banach Journal of Mathematical Analysis

Relatively compact sets in variable-exponent Lebesgue spaces

Rovshan Bandaliyev and Przemysław Górka

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We study totally bounded sets in variable Lebesgue spaces. The full characterization of this kind of sets is given for the case of variable Lebesgue space on metric measure spaces. Furthermore, the sufficient conditions for compactness are shown without assuming log-Hölder continuity of the exponent.

Article information

Banach J. Math. Anal. Volume 12, Number 2 (2018), 331-346.

Received: 31 January 2017
Accepted: 12 May 2017
First available in Project Euclid: 19 December 2017

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Primary: 28C99: None of the above, but in this section
Secondary: 46B50: Compactness in Banach (or normed) spaces 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Lebesgue spaces with variable exponent metric measure spaces Riesz–Kolmogorov theorem


Bandaliyev, Rovshan; Górka, Przemysław. Relatively compact sets in variable-exponent Lebesgue spaces. Banach J. Math. Anal. 12 (2018), no. 2, 331--346. doi:10.1215/17358787-2017-0039.

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