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We consider reflexive Bergman spaces on polygonal domains Ω of the complex plane. With some restrictions to the angles of the boundary of Ω, we show that the boundedness of… Click to show full abstract
We consider reflexive Bergman spaces on polygonal domains Ω of the complex plane. With some restrictions to the angles of the boundary of Ω, we show that the boundedness of the Toeplitz operator with a positive symbol g is equivalent to the boundedness of the Berezin transform of g or to g times the area measure being a Carleson measure. The result is also formulated for more general simply connected domains. The main technical tool is a new weighted Forelli–Rudin-type estimate.
Keywords:
berezin transform;
transform toeplitz;
toeplitz operators;
polygonal domains
Journal Title: Complex Variables and Elliptic Equations
Year Published: 2021
Link to full text (if available)
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Journal Title: Complex Variables and Elliptic Equations
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!