Mapping Properties of Mixed Fractional Differentiation Operators in Hölder Spaces Defined by Usual Hölder Condition

Abstract

We study mixed fractional derivative in Marchaud form of function of two variables in Hölder spaces of different orders in each variables. We consider Hölder spaces defined both by first order differences in each variable and also by the mixed second order difference, the main interest being in the evaluation of the latter for the mixed fractional derivative in the cases Hölder class.