BOUNDED TOEPLITZ PRODUCTS ON WEIGHTED BERGMAN SPACES

BOUNDED TOEPLITZ PRODUCTS ON WEIGHTED BERGMAN SPACES

We consider the question for which square integrable analytic functions f and g on the unit disk the densely defined products TfTg̅ are bounded on the Bergman space. We prove results analogous to those we obtained in the setting of the unweighted Bergman space [17]. We will furthermore completely de...

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Veröffentlicht in:Journal of operator theory 2008-03, Vol.59 (2), p.277-308
Hauptverfasser: STROETHOFF, KAREL, ZHENG, DECHAO
Format: Artikel
Sprache:eng
Schlagworte:
Analytic functions
Cauchy Schwarz inequality
Dyadics
Inner products
Integers
Mathematical inequalities
Mathematical integrals
Necessary conditions
Rectangles
Sufficient conditions
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Zusammenfassung:We consider the question for which square integrable analytic functions f and g on the unit disk the densely defined products TfTg̅ are bounded on the Bergman space. We prove results analogous to those we obtained in the setting of the unweighted Bergman space [17]. We will furthermore completely describe when the Toeplitz product TfTg̅ is invertible or Fredholm and prove results generalizing those we obtained for the unweighted Bergman space in [18].
ISSN:0379-4024
1841-7744