On isomorphism implemented by mixed fractional integrals in hölder spaces
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.