Banach Journal of Mathematical Analysis

Relatively compact sets in variable-exponent Lebesgue spaces

Rovshan Bandaliyev and Przemysław Górka

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Abstract

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

Source
Banach J. Math. Anal. (2018), 16 pages.

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

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1513674117

Digital Object Identifier
doi:10.1215/17358787-2017-0039

Subjects
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.)

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

Citation

Bandaliyev, Rovshan; Górka, Przemysław. Relatively compact sets in variable-exponent Lebesgue spaces. Banach J. Math. Anal., advance publication, 19 December 2017. doi:10.1215/17358787-2017-0039. https://projecteuclid.org/euclid.bjma/1513674117


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