Abstract
Recall that by Theorems 10.4.9 and 10.5.1, the function
is responsible for the boundedness of a Toeplitz operator with symbol a=a(y). If \( a = a\left( y \right) \in L_\infty \left( {\mathbb{R}_ + } \right) \), then the operator Ta(λ) is obviously bounded on all spaces \( \mathcal{A}_\lambda ^2 \left( \Pi \right) \), where λ∈(−1, ∞), and the corresponding norms are uniformly bounded by sup z |a(z)|. That is, all spaces \( \mathcal{A}_\lambda ^2 \left( \Pi \right) \), where λ∈(−1, ∞), are natural and appropriate for Toeplitz operators with bounded symbols. One of our aims is a systematic study of unbounded symbols. To avoid unnecessary technicalities in this chapter we will always assume that λ∈[0, ∞).
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© 2008 Birkhäuser Verlag AG
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(2008). Dynamics of Properties of Toeplitz Operators on the Upper Half-Plane: Parabolic Case. In: Commutative Algebras of Toeplitz Operators on the Bergman Space. Operator Theory: Advances and Applications, vol 185. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8726-6_13
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DOI: https://doi.org/10.1007/978-3-7643-8726-6_13
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8725-9
Online ISBN: 978-3-7643-8726-6
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