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- W1497248431 abstract "We show that the norm of the vector of Riesz transforms as operator in the weighted Lebesgue space Lω2 is bounded by a constant multiple of the first power of the Poisson-A2 characteristic of ω. The bound is free of dimension and optimal. 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 Lωp for 1<p<∞ are discussed. Our arguments to exhibit sharpness at the critical exponent p=2 require a martingale extrapolation theorem, for which we provide a proof. We also show that for n>1, the Poisson-A2 class is properly included in the classical A2 class." @default.
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- W1497248431 date "2017-07-01" @default.
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- W1497248431 title "A linear dimensionless bound for the weighted Riesz vector" @default.
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- W1497248431 doi "https://doi.org/10.1016/j.bulsci.2017.05.004" @default.
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