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

Olsen, Jan Fredrik LU and Reguera, María Carmen (2016) In Revista Matematica Iberoamericana 32(2). p.495-510
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.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Bergman spaces, De saint-venant inequality, Hankel operators, Isoperimetric inequality., Putnam's inequality
in
Revista Matematica Iberoamericana
volume
32
issue
2
pages
16 pages
publisher
EMS Publishing House
external identifiers
  • scopus:84973902173
  • wos:000383355100005
ISSN
0213-2230
DOI
10.4171/rmi/892
language
English
LU publication?
yes
id
1c811b94-e4be-420f-9848-607faeeb4c09
date added to LUP
2017-02-22 14:54:41
date last changed
2017-09-18 11:34:33
@article{1c811b94-e4be-420f-9848-607faeeb4c09,
  abstract     = {<p>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.</p>},
  author       = {Olsen, Jan Fredrik and Reguera, María Carmen},
  issn         = {0213-2230},
  keyword      = {Bergman spaces,De saint-venant inequality,Hankel operators,Isoperimetric inequality.,Putnam's inequality},
  language     = {eng},
  number       = {2},
  pages        = {495--510},
  publisher    = {EMS Publishing House},
  series       = {Revista Matematica Iberoamericana},
  title        = {On a sharp estimate for hankel operators and Putnam's inequality},
  url          = {http://dx.doi.org/10.4171/rmi/892},
  volume       = {32},
  year         = {2016},
}