Fractional integration in weighted Lebesgue spaces. (English. Russian original) Zbl 1468.26003
J. Contemp. Math. Anal., Armen. Acad. Sci. 56, No. 2, 57-67 (2021); translation from Izv. Nats. Akad. Nauk Armen., Mat. 56, No. 2, 3-17 (2021).
Summary: The action of the fractional integration operator in weighted Lebesgue classes and mixed-norm spaces is studied in the unit ball from \({\mathbb{R}}^n \). Some results of Hardy, Littlewood, and Flett are refined and generalized.
MSC:
| 26A33 | Fractional derivatives and integrals |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
Keywords:
fractional integration; fractional differentiation; weighted Lebesgue spaces; mixed-norm spacesReferences:
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