Back to Search
Start Over
Riesz-Kolmogorov theorem in variable exponent Lebesgue spaces and its applications to Riemann-Liouville fractional differential equations
- Source :
- Science China Mathematics. 61:1807-1824
- Publication Year :
- 2018
- Publisher :
- Springer Science and Business Media LLC, 2018.
-
Abstract
- In this paper, we obtain the necessary and sufficient condition of the pre-compact sets in the variable exponent Lebesgue spaces, which is also called the Riesz-Kolmogorov theorem. The main novelty appearing in this approach is the constructive approximation which does not rely on the boundedness of the Hardy-Littlewood maximal operator in the considered spaces such that we do not need the log-Holder continuous conditions on the variable exponent. As applications, we establish the boundedness of Riemann-Liouville integral operators and prove the compactness of truncated Riemann-Liouville integral operators in the variable exponent Lebesgue spaces. Moreover, applying the Riesz-Kolmogorov theorem established in this paper, we obtain the existence and the uniqueness of solutions to a Cauchy type problem for fractional differential equations in variable exponent Lebesgue spaces.
- Subjects :
- Mathematics::Functional Analysis
Pure mathematics
Variable exponent
General Mathematics
010102 general mathematics
Mathematics::Classical Analysis and ODEs
Cauchy distribution
Type (model theory)
01 natural sciences
Constructive
010101 applied mathematics
Compact space
Uniqueness
0101 mathematics
Fractional differential
Lp space
Mathematics
Subjects
Details
- ISSN :
- 18691862 and 16747283
- Volume :
- 61
- Database :
- OpenAIRE
- Journal :
- Science China Mathematics
- Accession number :
- edsair.doi...........ec192ff4cc056a19781710068cfce2d3