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arXiv · 1411.1245

The behavior of the bounds of matrix-valued maximal inequality in $\mathbb{R}^n$ for large $n$

Guixiang Hong
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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 resut in the scalar-valued case. We also show that the weak type $(1,1)$ bound has similar behavior as Stein and Stömberg's.

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Guixiang Hong. 2014-11-05. The behavior of the bounds of matrix-valued maximal inequality in $\mathbb{R}^n$ for large $n$. https://arxiv.org/abs/1411.1245

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