Sharp bounds for fractional Hardy operator on higher-dimensional product spaces
Sharp bounds for fractional Hardy operator on higher-dimensional product spaces
复制标题
高维乘积空间上分数 Hardy 算子的锐界
DOI：
10.7523/j.issn.2095-6134.2020.01.001
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发表时间：
2020-01
期刊：
影响因子：
--
通讯作者：
Dunyan Yan
中科院分区：
文献类型：
--
作者：
Xiang Li;Mingquan Wei;Dunyan Yan
In this paper, we get the sharp bounds for fractional Hardy operator on higherdimensional product spaces from $ {{L}^{1}}\left( {{\mathbb{R}}^{{{n}_{1}}}}\times \cdots \times {{\mathbb{R}}^{{{n}_{m}}}} \right)$ to the space $ w{{L}^{\mathit{\boldsymbol{Q}}}}\left( {{\mathbb{R}}^{{{n}_{1}}}}\times \cdots \times {{\mathbb{R}}^{{{n}_{m}}}} \right)$ . More generally, the norm of fractional Hardy operator on higher-dimensional product spaces from $ {{L}^{\mathit{\boldsymbol{P}}}}\left( {{\mathbb{R}}^{{{n}_{1}}}}\times \cdots \times {{\mathbb{R}}^{{{n}_{m}}}} \right)$ to ${{L}^{{{\mathit{\boldsymbol{Q}}}_{I}}}}\left( {{\mathbb{R}}^{{{n}_{1}}}}\times \cdots \times {{\mathbb{R}}^{{{n}_{m}}}} \right) $ is obtained.
In this paper, we get the sharp bounds for fractional Hardy operator on higherdimensional product spaces from $ {{L}^{1}}\left( {{\mathbb{R}}^{{{n}_{1}}}}\times \cdots \times {{\mathbb{R}}^{{{n}_{m}}}} \right)$ to the space $ w{{L}^{\mathit{\boldsymbol{Q}}}}\left( {{\mathbb{R}}^{{{n}_{1}}}}\times \cdots \times {{\mathbb{R}}^{{{n}_{m}}}} \right)$ . More generally, the norm of fractional Hardy operator on higher-dimensional product spaces from $ {{L}^{\mathit{\boldsymbol{P}}}}\left( {{\mathbb{R}}^{{{n}_{1}}}}\times \cdots \times {{\mathbb{R}}^{{{n}_{m}}}} \right)$ to ${{L}^{{{\mathit{\boldsymbol{Q}}}_{I}}}}\left( {{\mathbb{R}}^{{{n}_{1}}}}\times \cdots \times {{\mathbb{R}}^{{{n}_{m}}}} \right) $ is obtained.