Toeplitz Operators with Radial Symbols on Weighted Pluriharmonic Bergman Spaces over Reinhardt Domains

Toeplitz Operators with Radial Symbols on Weighted Pluriharmonic Bergman Spaces over Reinhardt Domains

In this paper, we design an operator <i>A</i> restricted to a weighted pluriharmonic Bergman space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>b</mi><mi>...

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Bibliographic Details
Main Authors: Zhi-Ling Sun, Feng Qi, Wei-Shih Du
Format: Article
Language:English
Published: MDPI AG 2025-06-01
Series:Axioms
Subjects:
Toeplitz operators
weighted pluriharmonic Bergman space
radial symbol
Reinhardt domain
Online Access:https://www.mdpi.com/2075-1680/14/6/478
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Summary:In this paper, we design an operator <i>A</i> restricted to a weighted pluriharmonic Bergman space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>b</mi><mi>μ</mi><mn>2</mn></msubsup><mrow><mo>(</mo><mi mathvariant="normal">Ω</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> over the Reinhardt domains, with an isometric isomorphism between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>b</mi><mi>μ</mi><mn>2</mn></msubsup><mrow><mo>(</mo><mi mathvariant="normal">Ω</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and the subset of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>l</mi><mn>2</mn></msub><mrow><mo>(</mo><msup><mi mathvariant="double-struck">Z</mi><mi>n</mi></msup><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. Furthermore, we show that Toeplitz operators <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mi>a</mi></msub></semantics></math></inline-formula> with radial symbols are unitary to the multiplication operators <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>γ</mi><mi>a</mi></msub><mi>I</mi></mrow></semantics></math></inline-formula> on sequence space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>l</mi><mn>2</mn></msub></semantics></math></inline-formula> by using the operator <i>A</i>. The Wick function of a Toeplitz operator with a radial symbol provides some features to the operator, establishing its spectral decomposition. Finally, we specify the obtained results on the Reinhardt domains for the unit ball.
ISSN:2075-1680

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