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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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