@article{He2025, 
author = {Tianyang He and Zhiwen Liu and Ting Yu},
title = {The Weighted        L          p       estimates for the fractional Hardy operator and a class of integral operators on the Heisenberg group},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {1},
pages = {858-883},
keywords = {Hilbert operator, fractional Hardy operator, m-linear n-dimensional integral operator with a kernel, weighted Lebesgue space, Hardy-Littlewood-Pólya operator, sharp bound for the integral operator},
url = {https://www.sciopen.com/article/10.3934/math.2025041},
doi = {10.3934/math.2025041},
abstract = {In the setting of a Heisenberg group, we first studied the sharp weak estimate for the    n-dimensional fractional Hardy operator from        L    p   to        L          q      ,      ∞      . Next, we studied the sharp bounds for the    m-linear    n-dimensional integral operator with a kernel on weighted Lebesgue spaces. As an application, the sharp bounds for Hardy, Hardy-Littlewood-Pólya, and Hilbert operators on weighted Lebesgue spaces were obtained. Finally, according to the previous steps, we also found the estimate for the Hausdorff operator on weighted        L    p   spaces.}
}