Sharp bounds and T1 theorem for Calderón-Zygmund operators with matrix kernel on matrix weighted spaces

2017/05/17 by Sandra Pott, Pott, Sandra, Andrei Stoica +1
Mathematics · #42A50 #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1705.06105

openalex publication_date 2017/05/17 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

For a matrix A₂ weight W on R^p, we introduce a new notion of W-Calderón-Zygmund matrix kernels, following earlier work in by Isralowitz. We state and prove a T1 theorem for such operators and give a representation theorem in terms of dyadic W-Haar shifts and paraproducts, in the spirit of Hytönen's Representation Theorem. Finally, by means of a Bellman function argument, we give sharp bounds for such operators in terms of bounds for weighted matrix martingale transforms and paraproducts.

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