Geodesic
On one application of the Zygmund–Marcinkiewicz theorem
Matematičeskie zametki SVFU, Tome 27 (2020) no. 3, pp. 39-51 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we aim to generalize results obtained in the framework of fractional calculus due to reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained technique on practical problems connected with various physical and chemical processes. More precisely, a class of existence and uniqueness theorems is covered, the most remarkable representative of which is the existence and uniqueness theorem for the Abel equation in a weighted Lebesgue space. The method of proof corresponding to the uniqueness part is worth noticing separately: it reveals properties of the operator as well as properties of the space into which it acts and emphasizes their relationship.
Keywords: Riemann–Liouville operator, weighted Lebesgue space.
Mots-clés : Abel equation, Jacobi polynomial 
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     author = {M. V. Kukushkin},
     title = {On one application of the {Zygmund{\textendash}Marcinkiewicz} theorem},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {39--51},
     year = {2020},
     volume = {27},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2020_27_3_a3/}
}
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M. V. Kukushkin. On one application of the Zygmund–Marcinkiewicz theorem. Matematičeskie zametki SVFU, Tome 27 (2020) no. 3, pp. 39-51. http://geodesic.mathdoc.fr/item/SVFU_2020_27_3_a3/