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Izv. RAN. Ser. Mat., 2014, Volume 78, Issue 5, Pages 27–52 (Mi izv8116)  

Modified Bessel ${\mathbf P}$-integrals and $\mathbf P$-derivatives and their properties

S. S. Volosivets

Saratov State University named after N. G. Chernyshevsky

Abstract: We study the modified Bessel ${\mathbf P}$-integral, whose properties are similar to those of the Bessel potential, and the modified Bessel ${\mathbf P}$-derivative. These operators are inverse to each other. We prove analogues of the embedding theorems of Hardy, Littlewood, Stein, Zygmund and Lizorkin concerning the images of $L^p(\mathbb R)$ under the action of Bessel potentials. We give applications of the Bessel integral and derivative to the integrability of the ${\mathbf P}$-adic Fourier transform and to approximation theory (an embedding theorem of Ul'yanov type).

Keywords: Bessel potential, modified Bessel $\mathbf P$-derivative, $\mathbf P$-adic Hölder–Besov spaces, $\mathbf P$-adic distributions, $\mathbf P$-adic BMO space, embedding theorem of Ul'yanov type.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.1520.2014/K


DOI: https://doi.org/10.4213/im8116

Full text: PDF file (679 kB)
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English version:
Izvestiya: Mathematics, 2014, 78:5, 877–901

Bibliographic databases:

UDC: 517.518
MSC: 26A33, 41A30, 42C10, 43A15, 43A25, 43A70
Received: 06.03.2013
Revised: 17.07.2013

Citation: S. S. Volosivets, “Modified Bessel ${\mathbf P}$-integrals and $\mathbf P$-derivatives and their properties”, Izv. RAN. Ser. Mat., 78:5 (2014), 27–52; Izv. Math., 78:5 (2014), 877–901

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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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