RT Journal Article
T1 Representation and inequalities involving continuous linear functionals and fractional derivatives
A1 Jornet, Marc
A1 Nieto Roig, Juan José
K1 Representation of functionals
K1 Inequalities
K1 Differintegral operators
K1 Riemann-Liouville fractional calculus
AB We investigate how continuous linear functionals can be represented in terms of generic operators and certain kernels (Peano kernels), and we study lower bounds for the operators as a consequence, in the space of square-integrable functions. We apply and develop the theory for the Riemann–Liouville fractional derivative (an inverse of the Riemann–Liouville integral), where inequalities are derived with the Gaussian hypergeometric function. This work is inspired by the recent contributions by Fernandez and Buranay (J Comput Appl Math 441:115705, 2024) and Jornet (Arch Math, 2024).
PB Springer
YR 2024
FD 2024-10-29
LK https://hdl.handle.net/10347/46490
UL https://hdl.handle.net/10347/46490
LA eng
NO Jornet, M., & Nieto, J. J. (2025). Representation and inequalities involving continuous linear functionals and fractional derivatives. Advances in Operator Theory, 10(1). https://doi.org/10.1007/S43036-024-00397-8
NO The research of the author Juan J. Nieto was supported by the Agencia Estatal de Investigación (AEI) of Spain Grant PID2020-113275GB-I00 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”, by the “European Union” and Xunta de Galicia, grant ED431C 2023/12 for Competitive Reference Research Groups (2023–2026).
DS Minerva
RD 19 may 2026