Weighted estimates for operators of fractional integration of variable order in generalized variable Hölder spaces.

The paper is devoted to weighted estimates for operators of fractional integration of variable order of Bergman type in generalized variable Hölder spaces of holomorphic functions on the unit disc D . Due to the choice of the weight, we can include in consideration the case when the real part of the complex power of the operator degenerates. We prove the estimates of Zygmund type for the modulus of continuity, and then we obtain the corresponding weighted boundedness result. [ABSTRACT FROM AUTHOR]