Abstract
In this paper, we study the behavior of the bounds of matrix-valued maximal inequality in $\mathbb{R}^{n}$ for large $n$. The main result of this paper is that the $L_{p}$-bounds ($p>1$) can be taken to be independent of $n$, which is a generalization of Stein and Strömberg’s result in the scalar-valued case. We also show that the weak type $(1,1)$ bound has similar behavior as Stein and Stömberg’s.
Citation
Guixiang Hong. "The behavior of the bounds of matrix-valued maximal inequality in $\mathbb{R}^{n}$ for large $n$." Illinois J. Math. 57 (3) 855 - 869, Fall 2013. https://doi.org/10.1215/ijm/1415023514
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