Geodesic
Partial integral operators of non-negative orders in weighted Lebesgue spaces
Čelâbinskij fiziko-matematičeskij žurnal, Tome 6 (2021) no. 3, pp. 289-298 Cet article a éte moissonné depuis la source Math-Net.Ru

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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/

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