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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2022, Volume 204, Pages 97–103
DOI: https://doi.org/10.36535/0233-6723-2022-204-97-103
(Mi into945)
 

Theorems on iterations of partial integrals in a space with mixed norm

L. N. Lyakhovab, N. I. Trusovaa

a Lipetsk State Pedagogical University
b Voronezh State University
References:
Abstract: In $\mathbb{R}_2$, we consider partial integrals acting on the first or second variable and obtain conditions for bounded action in spaces of continuous functions with respect to one of the variables with values in the Lebesgue class $L_p$ with respect to the other variable. We assume that these functions are defined in a finite rectangle $D\in\mathbb{R}_2$. We prove theorems on the boundedness of iterations of these partial integrals in the spaces of anisotropic functions $C(D_\alpha^{(1)}; L_p(D_{\overline{\alpha}}^{(1)}))$, where $\alpha$ and $\overline{\alpha}$ are indices complementing each other up to the double index $(1;2)$.
Keywords: partial integral, anisotropic function space, mixed norm.
Funding agency Grant number
Russian Foundation for Basic Research 19-41-480002
This work was supported by the Russian Foundation for Basic Research and (project No. 19-41-480002).
Document Type: Article
UDC: 517.98
MSC: 45B99, 47G99
Language: Russian
Citation: L. N. Lyakhov, N. I. Trusova, “Theorems on iterations of partial integrals in a space with mixed norm”, Proceedings of the Voronezh spring mathematical school  "Modern methods of the theory of boundary-value problems. Pontryagin  readings – XXXI". Voronezh, May 3-9, 2020, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 204, VINITI, Moscow, 2022, 97–103
Citation in format AMSBIB
\Bibitem{LyaTru22}
\by L.~N.~Lyakhov, N.~I.~Trusova
\paper Theorems on iterations of partial integrals in a space with mixed norm
\inbook Proceedings of the Voronezh spring mathematical school 
"Modern methods of the theory of boundary-value problems. Pontryagin  readings – XXXI".
Voronezh, May 3-9, 2020
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2022
\vol 204
\pages 97--103
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into945}
\crossref{https://doi.org/10.36535/0233-6723-2022-204-97-103}
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