Geodesic
Theorems on iterations of partial integrals in a space with mixed norm
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings – XXXI". Voronezh, May 3-9, 2020, Tome 204 (2022), pp. 97-103

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In $\mathbb{R}_2$, we consider partial integrals acting on the first or second variable and obtain conditions for bounded action in spaces of continuous functions with respect to one of the variables with values in the Lebesgue class $L_p$ with respect to the other variable. We assume that these functions are defined in a finite rectangle $D\in\mathbb{R}_2$. We prove theorems on the boundedness of iterations of these partial integrals in the spaces of anisotropic functions $C(D_\alpha^{(1)}; L_p(D_{\overline{\alpha}}^{(1)}))$, where $\alpha$ and $\overline{\alpha}$ are indices complementing each other up to the double index $(1;2)$.
Keywords: partial integral, anisotropic function space, mixed norm. 
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     author = {L. N. Lyakhov and N. I. Trusova},
     title = {Theorems on iterations of partial integrals in a space with mixed norm},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {97--103},
     publisher = {mathdoc},
     volume = {204},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_204_a9/}
}
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L. N. Lyakhov; N. I. Trusova. Theorems on iterations of partial integrals in a space with mixed norm. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings – XXXI". Voronezh, May 3-9, 2020, Tome 204 (2022), pp. 97-103. http://geodesic.mathdoc.fr/item/INTO_2022_204_a9/