Abstract
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 \( {\mathbb {D}} \). 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.
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Acknowledgements
The work was done at the Regional Scientific and Educational Mathematical Center of Southern Federal University with the support of the Ministry of Education and Science of Russia, Agreement No. 075-02-2022-893. Alexey Karapetyants is partially supported by the Russian Foundation for Fundamental Research, Project 20-51-46003-a.
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Karapetyants, A., Morales, E. Weighted estimates for operators of fractional integration of variable order in generalized variable Hölder spaces. Fract Calc Appl Anal 25, 1250–1259 (2022). https://doi.org/10.1007/s13540-022-00040-4
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DOI: https://doi.org/10.1007/s13540-022-00040-4
Keywords
- Fractional calculus (primary)
- Operators of fractional integration of variable order
- Holder spaces
- Zygmund estimates