Abstract
We study mixed Riemann-Liouville fractional integration operators and mixed fractional derivative in Marchaud form of function of two variables in Hölder spaces of different orders in each variables. The obtained are results generalized to the case of Hölder spaces with power weight.
Highlights
In1928 H.G.Hardy and J.E.Littlewood [1] showed that the fractional integral I x x 0 t dt x t 10 x 1 of order 0,1 improves the Hölder behavior of its density exactly by the order
These operators establish an isomorphism between the spaces under the condition. This result was extended in many directions: to the case of Hölder spaces with power weight [15] to the case of generalized Hölder spaces with characteristics from the Bari-Stechkin class [13]
The obtained results generalized to the case of Hölder spaces with power weight of functions of two variables
Summary
In1928 H.G.Hardy and J.E.Littlewood [1] (see [13], Theorem 3.1 and 3.2) showed that the fractional integral. 0 x 1 of order 0,1 improves the Hölder behavior of its density exactly by the order These operators establish an isomorphism between the spaces. The statement about the properties of a map in Hölder spaces for a mixed fractional. The Riemann-Liouville fractional integration operator establishes an isomorphism between weighted. Integration operators and mixed fractional derivative in Marchaud form of function of two variables in Hölder spaces of different orders in each variables. The obtained results generalized to the case of Hölder spaces with power weight of functions of two variables
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