Revista Matemática Iberoamericana

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Volume 32, Issue 2, 2016, pp. 495–510
DOI: 10.4171/RMI/892

Published online: 2016-06-08

On a sharp estimate for Hankel operators and Putnam’s inequality

Jan-Fredrik Olsen[1] and María Carmen Reguera[2]

(1) Lund University, Sweden
(2) University of Birmingham, UK

We obtain a sharp norm estimate for Hankel operators with anti-analytic symbol for weighted Bergman spaces. For the classical Bergman space, the estimate improves the corresponding classical Putnam inequality for commutators of Toeplitz operators with analytic symbol by a factor of 1/2, answering a recent conjecture by Bell, Ferguson and Lundberg. As an application, this yields a new proof of the de Saint-Venant inequality, which relates the torsional rigidity of a domain with its area.

Keywords: Bergman spaces, Hankel operators, Putnam’s inequality, de Saint-Venant inequality, isoperimetric inequality

Olsen Jan-Fredrik, Reguera María Carmen: On a sharp estimate for Hankel operators and Putnam’s inequality. Rev. Mat. Iberoam. 32 (2016), 495-510. doi: 10.4171/RMI/892