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arXiv · 1705.06105

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

Sandra Pott·Andrei Stoica
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Abstract

For a matrix A_2 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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Sandra Pott, Andrei Stoica. 2017-05-17. Sharp bounds and T1 theorem for Calderón-Zygmund operators with matrix kernel on matrix weighted spaces. https://arxiv.org/abs/1705.06105

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