A linear dimensionless bound for the weighted Riesz vector

作者：Domelevo Komla; Petermichl Stefanie^*; Wittwer Janine

来源：Bulletin des Sciences Mathematiques, 2017, 141(5): 385-407.

DOI：10.1016/j.bulsci.2017.05.004

• Bellman function
• Riesz transforms
• Weighted estimates
• Background noise

We show that the norm of the vector of Riesz transforms as operator in the weighted Lebesgue space L-w(2) is bounded by a constant multiple of the first power of the Poisson-A(2) characteristic of w. 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 L-w(p) for 1 < p < infinity 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-A(2) class is properly included in the classical A(2) class.

• 出版日期2017-7