On a sharp estimate for Hankel operators and Putnam’s inequality
Jan-Fredrik Olsen
Lund University, SwedenMaría Carmen Reguera
University of Birmingham, UK
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Abstract
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.
Cite this article
Jan-Fredrik Olsen, María Carmen Reguera, On a sharp estimate for Hankel operators and Putnam’s inequality. Rev. Mat. Iberoam. 32 (2016), no. 2, pp. 495–510
DOI 10.4171/RMI/892