Characterization of the range of one-dimensional fractional integration in the space with variable exponent. (English) Zbl 1160.46022
Bastos, Maria Amélia (ed.) et al., Operator algebras, operator theory and applications. Selected papers of the international summer school and workshop, WOAT 2006, Lisbon, Portugal, September 1–5, 2006. Basel: Birkhäuser (ISBN 978-3-7643-8683-2/hbk). Operator Theory: Advances and Applications 181, 393-416 (2008).
Summary: Within the frameworks of weighted Lebesgue spaces with variable exponent, we give a characterization of the range of the one-dimensional Riemann-Liouville fractional integral operator in terms of convergence of the corresponding hypersingular integrals. We also show that this range coincides with the weighted Sobolev-type space \(L^{\alpha,p(\cdot)}[(a, b),\rho]\).
For the entire collection see [Zbl 1140.46001].
For the entire collection see [Zbl 1140.46001].
MSC:
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
| 47B38 | Linear operators on function spaces (general) |
| 26A33 | Fractional derivatives and integrals |
