Fractional Integro-Differentiation of the Complex Order in Generalized Holder Spaces

To the Memory of Professor Nikolai Karapetiants: Life and Scientific Heritage

“…In the papers [82][83][84][85][86] in collaboration with B. G. Vakulov and L. D. Shankishvili, Professor Karapetiants explored spherical potentials of complex order, spherical hypersingular integrals in generalized Hölder spaces and spherical convolution operators with a power-logarithmic kernel. In [77][78][79][80] the operators of the integro-differentiation of complex order, in particular, purely imaginary order, in generalized weighted Hölder spaces were studied.…”

Hardy-Littlewood-Type Theorem for Mixed Fractional Integrals in Hölder Spaces

“…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], [14]; to the case of more general weights [16], [17], etc. Different proofs were suggested in [2], [3], where the case of complex fractional orders was also considered the shortest proof being given in [2].…”