Geodesic
Boundedness of operators with partial integrals with the mixed norm. II
Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 3, pp. 293-305.

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The general form of a linear integral operator with partial integrals in $\mathbb{R}_3$ is considered as the sum of eight integral expressions, including partial integrals for one and two variables. The action of the specified operator is studied within the space $C(\Omega_1;L_{p}(\Omega_2))$ of continuous functions on $\overline{\Omega_1}$ with values in the Lebesgue class $L_p (\Omega_2)$, $1$, where $\Omega_1\times\Omega_2=D$ is the the finite parallelepiped in $\mathbb{R}_3$. We prove that the considered operators belong to the class of linear bounded operators from the anisotropic class of Lebesgue functions $L_{p,p^2}$ to the class of functions with the mixed norm $C (\Omega_1;L_{p}(\Omega_2))$.
Keywords: function with values in a Banach space, partial integral, linear operator with partial integrals, anisotropic classes of Lebesgue functions. 
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L. N. Lyakhov; N. I. Trusova. Boundedness of operators with partial integrals with the mixed norm. II. Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 3, pp. 293-305. http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_3_a3/

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