Geodesic
Boundedness of operators with partial integrals with the mixed norm. I
Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 1, pp. 22-31

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Two types of linear integral operators with partial integrals are considered, which are defined on functions given in a finite rectangle $D=D_1\times D_2$ of the Euclidean point space $\mathbb{R}_2$. Operators of the first type are constructed according to the type of Romanovsky integrals and are studied in the space $C(D_1;L_{p}(D_2))$ norms, space of continuous functions on $\overline{D_1}$ with values in the Lebesgue class $L_p(D_2)$. For general operators, the authors prove that they belong to the class of linear bounded operators from the anisotropic class of functions $L_{p,p^2}$ for $p>1$ to the class of functions with a mixed norm $C (D_1;L_{p}(D_2))$.
Keywords: function with values in a Banach space, partial integral, linear operator with partial integrals, Romanovsky partial integral, anisotropic classes of Lebesgue functions. 
@article{CHFMJ_2020_5_1_a1,
     author = {L. N. Lyakhov and N. I. Trusova},
     title = {Boundedness of operators with partial integrals with the mixed norm. {I}},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {22--31},
     publisher = {mathdoc},
     volume = {5},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_1_a1/}
}
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L. N. Lyakhov; N. I. Trusova. Boundedness of operators with partial integrals with the mixed norm. I. Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 1, pp. 22-31. http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_1_a1/