Notes on Matrix Valued Paraproducts

2005/12/16 by Tao Mei, Mei, Tao
Computer Science · Mathematics · #42B25 47B38) #47B35 (46L50 #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Numerical methods in inverse problems #math.CA #math.FA #msc:42B25 #msc:47B35

paper · pdf · doi:10.48550/arxiv.math/0512407

12 pages

openalex publication_date 2005/12/16 · arxiv created 2006/01/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Denote by M_n the algebra of n× n matrices. We consider the dyadic paraproducts π_b associated with M_n valued functions b, and show that the L^∞ (M_n) norm of b does not dominate ||π_b||_{L²(ℓ n²)→ L²(ℓn²)} uniformly over n. We also consider paraproducts associated with noncommutative martingales and prove that their boundedness on bounded noncommutative L^p-% martingale spaces implies their boundedness on bounded noncommutative L^q-% martingale spaces for all 1<p<q<∞ .

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