论文标题
与简单相关的多线性最大运算符
Multilinear maximal operators associated to simplices
论文作者
论文摘要
We establish $L^{p_1}\times\cdots\times L^{p_k}\to L^r$ and $\ell^{p_1}\times\cdots\times \ell^{p_k}\to \ell^r$ type bounds for multilinear maximal operators associated to averages over isometric copies of a given non-degenerate $ k $ -simplex在连续和离散的设置中。这些为Stein的球形最大运算符和离散的球形最大运算符提供了$ l^p \至l^p $的自然扩展和$ \ ell^p \ to \ ell^p $界限，每个结果都作为相应证明的关键成分。
We establish $L^{p_1}\times\cdots\times L^{p_k}\to L^r$ and $\ell^{p_1}\times\cdots\times \ell^{p_k}\to \ell^r$ type bounds for multilinear maximal operators associated to averages over isometric copies of a given non-degenerate $k$-simplex in both the continuous and discrete settings. These provide natural extensions of $L^p\to L^p$ and $\ell^p\to \ell^p$ bounds for Stein's spherical maximal operator and the discrete spherical maximal operator, with each of these results serving as a key ingredient of the respective proofs.
