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

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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/}
}
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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/