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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{CHFMJ_2021_6_3_a2,
     author = {L. N. Lyakhov and N. I. Trusova},
     title = {Partial integral operators of non-negative orders in weighted {Lebesgue} spaces},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {289--298},
     publisher = {mathdoc},
     volume = {6},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2021_6_3_a2/}
}
TY  - JOUR
AU  - L. N. Lyakhov
AU  - N. I. Trusova
TI  - Partial integral operators of non-negative orders in weighted Lebesgue spaces
JO  - Čelâbinskij fiziko-matematičeskij žurnal
PY  - 2021
SP  - 289
EP  - 298
VL  - 6
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHFMJ_2021_6_3_a2/
LA  - ru
ID  - CHFMJ_2021_6_3_a2
ER  - 
%0 Journal Article
%A L. N. Lyakhov
%A N. I. Trusova
%T Partial integral operators of non-negative orders in weighted Lebesgue spaces
%J Čelâbinskij fiziko-matematičeskij žurnal
%D 2021
%P 289-298
%V 6
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHFMJ_2021_6_3_a2/
%G ru
%F CHFMJ_2021_6_3_a2
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/