Opuscula Math. 39, no. 5 (2019), 705-731
https://doi.org/10.7494/OpMath.2019.39.5.705

Opuscula Mathematica

# On the Lebesgue and Sobolev spaces on a time-scale

Ewa Skrzypek
Katarzyna Szymańska-Dębowska

Abstract. We consider the generalized Lebesgue and Sobolev spaces on a bounded time-scale. We study the standard properties of these spaces and compare them to the classical known results for the Lebesgue and Sobolev spaces on a bounded interval. These results provide the necessary framework for the study of boundary value problems on bounded time-scales.

Keywords: Lebesgue spaces, Sobolev spaces, modular spaces, time-scales, boundary value problems on time-scales.

Mathematics Subject Classification: 26E70, 46B10.

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• Communicated by Marek Galewski.
• Revised: 2018-12-23.
• Accepted: 2019-02-25.
• Published online: 2019-09-05.