Geodesic
On the boundedness of the integral convolution operator in a pair of classical Lebesgue spaces $L_p$ and $L_r$
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 83 (2023), pp. 52-58

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In terms of the kernel of an integral convolution operator, a constructive criterion for its boundedness in a pair of classical Lebesgue spaces $L_p$ and $L_r$ is obtained. It is shown that in order for the integral convolution operator to act boundedly from $L_p$ to $L_{r,p}$, it is necessary and sufficient that the kernel $K(t)$ of the operator belonged to the Marcinkiewicz space $M_{t^{1-1/q}}$.
Keywords: integral convolution operator, boundedness, boundedness criterion
Mots-clés : Lebesgue spaces 
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     author = {E. A. Pavlov and A. I. Furmenko},
     title = {On the boundedness of the integral convolution operator in a pair of classical {Lebesgue} spaces $L_p$ and $L_r$},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {52--58},
     publisher = {mathdoc},
     number = {83},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2023_83_a4/}
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E. A. Pavlov; A. I. Furmenko. On the boundedness of the integral convolution operator in a pair of classical Lebesgue spaces $L_p$ and $L_r$. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 83 (2023), pp. 52-58. http://geodesic.mathdoc.fr/item/VTGU_2023_83_a4/