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arXiv · 2607.10154

The Weighted $\boldsymbol{L}^{\boldsymbol{p}}$ estimates for the fractional Hardy operator and a class of integral operators on the Heisenberg group

Tianyang He·Zhiwen Liu·Ting Yu
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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 $L^{q,\infty}$. 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-P\'{o}lya, 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.

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Tianyang He, Zhiwen Liu, Ting Yu. 2026-07-11. The Weighted $\boldsymbol{L}^{\boldsymbol{p}}$ estimates for the fractional Hardy operator and a class of integral operators on the Heisenberg group. https://doi.org/10.3934/math.2025041

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