海森堡群上分数阶哈代算子和一类积分算子的加权$\boldsymbol{L}^{\boldsymbol{p}}$估计
The Weighted $\boldsymbol{L}^{\boldsymbol{p}}$ estimates for the fractional Hardy operator and a class of integral operators on the Heisenberg group
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中文总结 AI 辅助
研究海森堡群上分数阶哈代算子等的加权$\boldsymbol{L}^{\boldsymbol{p}}$估计，通过研究$n$维分数阶哈代算子弱估计、$m$线性积分算子界等，得到哈代等算子在加权勒贝格空间的精确界及豪斯多夫算子在加权$L^p$空间的估计。
中文摘要 AI 辅助
在海森堡群的背景下，我们首先研究了从$L^p$到$L^{q,\infty}$的$n$维分数阶哈代算子的精确弱估计。接着，研究了具有核的$m$线性$n$维积分算子在加权勒贝格空间上的精确界。作为应用，得到了加权勒贝格空间上哈代、哈代 - 利特伍德 - 波利亚和希尔伯特算子的精确界。最后，根据前面步骤，还得到了加权$L^p$空间上豪斯多夫算子的估计。
英文摘要
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-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.
