SOME PROPERTIES OF MIXED FRACTIONAL INTEGRO-DIFFERENTIATION OPERATORS IN HÖLDER SPACES

Abstract

As is known, the Riemann-Liouville fractional integration operator establishes an isomorphism between Hölder spaces for functions one variable. 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.

Key words: functions of two variables, fractional derivative of Marchaud form, mixed fractional derivative, mixed fractional integral, Hölder space.