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

• Jan-Fredrik Olsen ^[1] ; María Carmen Reguera ^[2]
  1. [1] Lund University

     Lund University

     Suecia

     
  2. [2] University of Birmingham

     University of Birmingham

     Reino Unido

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 32, Nº 2, 2016, págs. 495-510
• Idioma: inglés
• DOI: 10.4171/RMI/892
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.