Geodesic
Partial integral operators of non-negative orders in weighted Lebesgue spaces
Čelâbinskij fiziko-matematičeskij žurnal, Tome 6 (2021) no. 3, pp. 289-298.

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We study a weighted partial integral operator in a weighted Lebesgue space $L_p^{\gamma}(D)$ with a measure of integration $d\mu_\gamma(x)=x^\gamma dx$ in $\mathbb{R}_2 $ and $\mathbb{R}_n$. The concept of the order of a weighted partial integral operator is introduced. A sufficient condition for such operators to be bounded in $L_p^\gamma$ is obtained.
Keywords: partial integral operator, weighted partial integral operator, weighted anisotropic Lebesgue space. 
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L. N. Lyakhov; N. I. Trusova. Partial integral operators of non-negative orders in weighted Lebesgue spaces. Čelâbinskij fiziko-matematičeskij žurnal, Tome 6 (2021) no. 3, pp. 289-298. http://geodesic.mathdoc.fr/item/CHFMJ_2021_6_3_a2/

[1] Schwartz L., Mathematical methods for physical sciences, Mir, Moscow, 1965 (In Russ.)

[2] Lyakhov L.N., Sanina E.L., “Kipriyanov — Beltrami operator with negative dimension of the Bessel operators and the singular Dirichlet problem for the $B$-harmonic equation”, Differential equations, 56:12 (2020), 1564–1574 | DOI | Zbl

[3] Appell J. M., Kalitvin A. S., Zabrejko P. P., Partial Integral Operators and Integro-Differential Equations, Marcel Dekker, New York, 2000 | Zbl

[4] Kalitvin A.S., Frolova E.V., Lineynye uravneniya s chastnymi integralami. C-teoriya, Lipetsk State Pedagogical University, Lipetsk, 2004 (In Russ.)

[5] Bessov O.V., Ilyin V.P., Nikolsky S.M., Integral representations of functions and embedding theorems, Nauka, Moscow,, 1975 (In Russ.)