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The sharp weighted bound for the Riesz transforms. (English) Zbl 1142.42005
The present work is concerned with the sharp bound for the operator norm of the Riesz transforms in $$L^2(\omega)$$. The sharp bound for other $$p$$ are also derived by means of extrapolation. S. Buckley [Mich. Math. J. 40, No. 1, 153–170 (1993; Zbl 0794.42011)] proved an $$L^2$$ bound in terms of the square of the classical $$A_2$$ characteristic of the weight, while A. K. Lerner [J. Funct. Anal. 232, No. 2, 477–494 (2006; Zbl 1140.42005)] established an improvement to $$3/2$$. In this paper, the author establishes the linear and best possible bound.

##### MSC:
 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.) 44A15 Special integral transforms (Legendre, Hilbert, etc.) 46E15 Banach spaces of continuous, differentiable or analytic functions
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##### References:
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