On isomorphism implemented by mixed fractional integrals in hölder spaces
International Journal of Development Research
On isomorphism implemented by mixed fractional integrals in hölder spaces
Received 17th February, 2019; Received in revised form 22nd March, 2019; Accepted 19th April, 2019; Published online 30th May, 2019
Copyright © 2019, Mamatov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
As is known, the Riemann-Liouville fractional integration operator establishes an isomorphism between Hölder spaces for functions one variables. We study mixed Riemann-Liouville fractional integration operats and mixed fractional derivative in Marchaud form of function of two variables in Hölder spaces of different orders in each variables. The obtained results extend the well known theorem of Hardy-Littlewood for one-dimensuianl fractional integrals to the case of mixed Hölderness.
