论文标题
在混合径向角度的耐强型操作员的急剧边界
Sharp bounds for Hardy-type operators on mixed radial-angular spaces
论文作者
论文摘要
在本文中，通过使用旋转方法，我们计算出与混合径向 - 角度空间上的$ n $二维操作员$ \ MATHCAL {h} $的尖锐绑定。此外，我们还获得了$ n $二维的刚性hardy操作员$ \ mathcal {h}_β$来自$ l^p_p_ {| x |}l_θ^{\ bar {p}}}（{\ bb r}^n）$ to to）美元通过使用二元性，还建立了双运算符的相应结果$ \ MATHCAL {H}^*$和$ \ MATHCAL {H}^*_β$。此外，还考虑了$ \ Mathcal {H} $的急剧弱型估计。
In this paper, by using the rotation method, we calculate that the sharp bound for $n$-dimensional Hardy operator $\mathcal{H}$ on mixed radial-angular spaces. Furthermore, we also obtain the sharp bound for $n$-dimensional fractional Hardy operator $\mathcal{H}_β$ from $L^p_{|x|}L_θ^{\bar{p}}({\Bbb R}^n)$ to $L^q_{|x|}L_θ^{\bar{q}}({\Bbb R}^n)$, where $0<β<n$, $1<p,q,\bar{p},\bar{q}<\infty$ and $1/p-1/q=β/n$. By using duality, the corresponding results for the dual operators $\mathcal{H}^*$ and $\mathcal{H}^*_β$ are also established. In addition, the sharp weak-type estimate for $\mathcal{H}$ is also considered.
