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arXiv · 1501.07880

A linear dimensionless bound for the weighted Riesz vector

Komla Domelevo·Stefanie Petermichl·Janine Wittwer
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Abstract

We show that the norm of the vector of Riesz transforms as operator in the weighted Lebesgue space L^2(w) is bounded by a constant multiple of the first power of the Poisson-A_2 characteristic of w. The bound is free of dimension. Our argument requires an extension of Wittwer's linear estimate for martingale transforms to the vector valued setting with scalar weights, for which we indicate a proof. Extensions to L^p(w) for 1 1, the Poisson-A_2 class is properly included in the classical A_2 class.

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Komla Domelevo, Stefanie Petermichl, Janine Wittwer. 2016-12-12. A linear dimensionless bound for the weighted Riesz vector. https://arxiv.org/abs/1501.07880

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