Sparse bounds for the bilinear spherical maximal function
Sparse bounds for the bilinear spherical maximal function
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DOI：
10.1112/jlms.12715
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发表时间：
2022-03
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影响因子：
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通讯作者：
Tainara Borges;B. Foster;Yumeng Ou;J. Pipher;Zirui Zhou
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作者：
Tainara Borges;B. Foster;Yumeng Ou;J. Pipher;Zirui Zhou
我们推导出稀疏边界的双线性球极大函数在任何维度d 1$d\geqslant1 $。当d ≠ 2 $d\geqslant 2$时，这立即恢复了算子的Lp×Lq→Lr$L^p\times L^q\rightarrow L^r$界，并蕴涵了关于双线性Muckenhoupt权的定量加权范数不等式，这似乎是该算子的第一个此类不等式.关键的创新是一组新开发的连续性Lp$L^p$改进估计的单尺度双线性球面平均算子。
We derive sparse bounds for the bilinear spherical maximal function in any dimension d⩾1$d\geqslant 1$ . When d⩾2$d\geqslant 2$ , this immediately recovers the sharp Lp×Lq→Lr$L^p\times L^q\rightarrow L^r$ bound of the operator and implies quantitative weighted norm inequalities with respect to bilinear Muckenhoupt weights, which seems to be the first of their kind for the operator. The key innovation is a group of newly developed continuity Lp$L^p$ improving estimates for the single‐scale bilinear spherical averaging operator.