Geodesic
Integral operators with periodic kernels in spaces of integrable functions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2020), pp. 3-9.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the integral operators with periodic kernels acting from $L_p(\mathbb{R}^n)$ to $L_q(\mathbb{R}^n)$. We obtain sufficient conditions for the boundedness of such operators. Moreover we obtain compactness conditions for the product of the integral operator with periodic kernel and the operator of multiplication by an essentially bounded function.
Keywords: integral operator, periodic kernel, boundedness, multiplication operator, compactness. 
@article{IVM_2020_2_a0,
     author = {O. G. Avsyankin},
     title = {Integral operators with periodic kernels in spaces of integrable functions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--9},
     publisher = {mathdoc},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_2_a0/}
}
TY  - JOUR
AU  - O. G. Avsyankin
TI  - Integral operators with periodic kernels in spaces of integrable functions
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2020
SP  - 3
EP  - 9
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2020_2_a0/
LA  - ru
ID  - IVM_2020_2_a0
ER  - 
%0 Journal Article
%A O. G. Avsyankin
%T Integral operators with periodic kernels in spaces of integrable functions
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2020
%P 3-9
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2020_2_a0/
%G ru
%F IVM_2020_2_a0
O. G. Avsyankin. Integral operators with periodic kernels in spaces of integrable functions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2020), pp. 3-9. http://geodesic.mathdoc.fr/item/IVM_2020_2_a0/

[1] Thieme H. R., “Renewal theorems for some mathematical models in epidemiology”, J. Integral Equat., 8:3 (1985), 185–216 | MR | Zbl

[2] Tsalyuk Z. B., “Integralnye uravneniya Volterra”, Itogi nauki i tekhniki. Ser. matem. anal., 15, 1977, 131–198 | Zbl

[3] Pulyaev V. F., Razvitie teorii lineinykh integralnykh uravnenii s periodicheskimi i pochti periodicheskimi yadrami, Diss. ... dokt. fiz.-matem. nauk, S.-Peterb. gos. un-t, Sankt-Peterburg, 2001

[4] Barsukova V. Yu., Pulyaev V. F., “Ob asimptotike resheniya integralnogo uravneniya na poluosi s periodicheskim yadrom”, Izv. vuzov. Severo-Kavkazskii region. Estestvennye nauki, 2003, no. 4, 3–5

[5] Barsukova V. Yu., Eksponentsialnye i ogranichennye resheniya lineinykh integralnykh uravnenii s periodicheskimi yadrami, Diss. ... kand. fiz.-matem. nauk, Rost. gos. un-t, Rostov-na-Donu, 2005

[6] Danford N., Shvarts Dzh., Lineinye operatory. Obschaya teoriya, IL, M., 1962

[7] Avsyankin O. G., Ulyanova L. V., “Ob ogranichennosti i kompaktnosti mnogomernykh integralnykh operatorov s periodicheskimi yadrami”, Izv. vuzov. Severo-Kavkazskii region. Estestvennye nauki, 2014, no. 1, 5–8 | MR

[8] Karapetyants N. K., “Ob odnom analoge teoremy Khermandera dlya oblastei, otlichnykh ot $\mathbb{R}^n$”, DAN SSSR, 293:6 (1987), 1294–1297 | MR | Zbl

[9] Karapetiants N. K., Samko S. G., Equations with involutive operators, Birkhäuser, Boston–Basel–Berlin, 2001 | MR | Zbl

[10] Avsyankin O. G., “Kompaktnost nekotorykh klassov operatorov tipa svertki v obobschennykh prostranstvakh Morri”, Matem. zametki, 104:3 (2018), 336–344 | DOI | MR | Zbl