Boundedness of operators with partial integrals with the mixed norm. II
Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 3, pp. 293-305
Voir la notice de l'article provenant de la source Math-Net.Ru
The general form of a linear integral operator with partial integrals in $\mathbb{R}_3$ is considered as the sum of eight integral expressions, including partial integrals for one and two variables. The action of the specified operator is studied within the space
$C(\Omega_1;L_{p}(\Omega_2))$ of
continuous functions on $\overline{\Omega_1}$ with values in the Lebesgue class $L_p (\Omega_2)$, $1$,
where $\Omega_1\times\Omega_2=D$ is the the finite parallelepiped in $\mathbb{R}_3$.
We prove that the considered operators belong to the class of linear bounded operators from the anisotropic class of Lebesgue functions $L_{p,p^2}$ to the class of functions with the mixed norm $C (\Omega_1;L_{p}(\Omega_2))$.
Keywords:
function with values in a Banach space, partial integral, linear operator with partial integrals, anisotropic classes of Lebesgue functions.
@article{CHFMJ_2020_5_3_a3,
author = {L. N. Lyakhov and N. I. Trusova},
title = {Boundedness of operators with partial integrals with the mixed norm. {II}},
journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
pages = {293--305},
publisher = {mathdoc},
volume = {5},
number = {3},
year = {2020},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_3_a3/}
}
TY - JOUR AU - L. N. Lyakhov AU - N. I. Trusova TI - Boundedness of operators with partial integrals with the mixed norm. II JO - Čelâbinskij fiziko-matematičeskij žurnal PY - 2020 SP - 293 EP - 305 VL - 5 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_3_a3/ LA - ru ID - CHFMJ_2020_5_3_a3 ER -
L. N. Lyakhov; N. I. Trusova. Boundedness of operators with partial integrals with the mixed norm. II. Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 3, pp. 293-305. http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_3_a3/