Hardy-Littlewood-Type Theorem for Mixed Fractional Integrals in Hölder Spaces
TulkinMamatov1, Nemat Mustafoev2, DilshodBarakaev3, RanoSabirova4
1TulkinMamatov, Department of Higher mathematics, Bukhara Technological Institute of Engineering, Bukhara, Uzbekistan.
2Nemat Mustafoev, Department of Higher mathematics, Bukhara Technological Institute of Engineering, Bukhara, Uzbekistan.
3DilshodBarakaev, Department of Higher mathematics, Bukhara Technological Institute of Engineering, Bukhara, Uzbekistan.
4RanoSabirova, Department of Higher mathematics, Bukhara Technological Institute of Engineering, Bukhara, Uzbekistan.
Manuscript received on 29 September 2021 | Revised Manuscript received on 10 October 2021 | Manuscript Accepted on 15 October 2021 | Manuscript published on 30 October 2021 | PP: 15-19 | Volume-1 Issue-2, October 2021 | Retrieval Number:100.1/ijam.B1105101221 | DOI: 10.54105/ijam.B1105.101221
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© The Authors. Published by Lattice Science Publication (LSP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
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.
Keywords: functions of two variables, fractional derivative of Marchaud form, mixed fractional derivative, weight, mixed fractional integral, Hölder space.
Scope of the Article: Differential Equations