TY - JOUR
T1 - Sharp Bound for the Generalized $m$-Linear $n$-Dimensional Hardy-Littlewood-Pόlya Operator
AU - He , Qianjun
AU - Wei , Mingquan
AU - Yan , Dunyan
JO - Analysis in Theory and Applications
VL - 1
SP - 28
EP - 41
PY - 2023
DA - 2023/03
SN - 39
DO - http://doi.org/10.4208/ata.OA-2020-0039
UR - https://global-sci.org/intro/article_detail/ata/21459.html
KW - Sharp bound, $n$-dimensional Hardy-Littlewood-Pόlya operator, power weight, Morrey space, Hausdorff operator.
AB - <p style="text-align: justify;">In this paper, we calculate the sharp bound for the generalized $m$-linear $n$-dimensional Hardy-Littlewood-Pόlya operator on power weighted central and noncentral homogeneous Morrey spaces. As an application, the sharp bound for the
Hardy-Littlewood-Pόlya operator on power weighted central and noncentral homogeneous Morrey spaces is obtained. Finally, we also find the sharp bound for the
Hausdorff operator on power weighted central and noncentral homogeneous Morrey
spaces, which generalizes the previous results.</p>