Complex Analysis and Operator Theory

, Volume 11, Issue 3, pp 707–726 | Cite as

Norm Estimates for Toeplitz Operators on the Bergman Space with Symbols Supported in Circles and Mixed Norms

  • Marcos López-García
  • Salvador Pérez-Esteva


In this paper we study the class of Toeplitz operators \(T_{\varphi }\), for which \(\int _{0}^{1}\left( 1-t\right) ^{q-1}\left\| T_{\varphi d\sigma _{t}}\right\| _{p}^{q}dt<\infty ,\) for \(1\le p,q<\infty ,\) where \(\varphi \in L^{1}(\mathbb {D}),\) \(\sigma _{t}\) is the Lebesgue measure in the circle \( |\xi |=t\) and \(\left\| \cdot \right\| _{p}\) is the p-Schatten norm of operators defined on the Bergman space of the disc. For that purpose we study the dependence on t of the norm and the p-Schatten norms of Toeplitz operators whose symbols are measures \(\mu \) supported in the circle \(tS^{1}\) with a positive density in \(L^{1}(tS^{1})\).


Toeplitz operators Bergman space Berezin Transform Mixed norms Schatten classes 

Mathematics Subject Classification

Primary 47B35 Secondary 46E30 



The authors would like to thank the anonymous reviewer for their valuable comments and suggestions.


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Instituto de Matemáticas, Unidad CuernavacaUniversidad Nacional Autónoma de MéxicoCuernavacaMexico

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