The behavior of the bounds of matrix-valued maximal inequality in ℝⁿ for large n

2014/11/05 by Guixiang Hong, Hong, Guixiang
Mathematics · #Advanced Harmonic Analysis Research #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1411.1245

Abstract

In this paper, we study the behavior of the bounds of matrix-valued maximal inequality in ℝⁿ 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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