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arXiv · 1305.5193

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

Jan-Fredrik Olsen·Maria Carmen Reguera
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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 St. Venant inequality, which relates the torsional rigidity of a domain with its area.

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Jan-Fredrik Olsen, Maria Carmen Reguera. 2014-05-23. On a sharp estimate for Hankel operators and Putnam's inequality. https://arxiv.org/abs/1305.5193

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