O. G. Avsyankin, F. G. Peretyat'kin, “On boundedness and compactness of multidimensional integral operators with homogeneous kernels”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, Number 11,Pages <nobr>64

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Brief communications

On boundedness and compactness of multidimensional integral operators with homogeneous kernels

O. G. Avsyankin, F. G. Peretyat'kin

Chair of Differential and Integral Equations, Southern Federal University, 8a Mil'chakov str., Rostov-on-Don, 344090 Russia

Abstract: We obtain sufficient conditions for the boundedness and compactness of multidimensional integral operators with homogeneous kernels acting from a weighted $L_p$-space to a weighted $L_q$-space.

Keywords: multidimensional integral operator, homogeneous kernel, boundedness, compactness.

UDC: 517.9

Presented by the member of Editorial Board: S. G. Samko
Received: 10.04.2013