Noncommutative weak (1,1) type estimate for a square function from ergodic theory

2019/07/31 by Guixiang Hong, Hong, Guixiang, Bang Xu +1
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1907.13499

openalex publication_date 2019/07/31 · openalex created_date 2019/08/13 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the boundedness of a square function from ergodic theory on noncommutative L_p-spaces. The main result is a weak (1,1) type estimate of this square function. We also show the (L_∞,BMO) estimate, and thus strong (L_p,L_p) estimate by interpolation. The main novel difficulty lies in the fact that the kernel of this square function does not enjoy any regularity, which is crucial in showing such endpoint estimates for standard noncommutative Calderón-Zygmund singular integral operators.

Citations

• A weak-type inequality for non-commutative martingales and applications

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