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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- Ewa Skrzypek
https://orcid.org/0000-0002-1234-915X- Lodz University of Technology, Institute of Mathematics, 90-924 Lodz, ul. Wólczanska 215, Poland
- Katarzyna Szymańska-Dębowska
- https://orcid.org/0000-0001-9252-380X
- Lodz University of Technology, Institute of Mathematics, 90-924 Lodz, ul. Wólczanska 215, Poland
- Communicated by Marek Galewski.
- Received: 2018-06-05.
- Revised: 2018-12-23.
- Accepted: 2019-02-25.
- Published online: 2019-09-05.
