Toeplitz Operators on the Weighted Pluriharmonic Bergman Space with Radial Symbols

Zhi Ling Sun and Yu Feng Lu

Abstract and Applied Analysis, 2011, vol. 2011, 1-15

Abstract:

We construct an operator ð ‘… whose restriction onto weighted pluriharmonic Bergman Space ð ‘ 2 𠜇 ( ð ”¹ ð ‘› ) is an isometric isomorphism between ð ‘ 2 𠜇 ( ð ”¹ ð ‘› ) and ð ‘™ # 2 . Furthermore, using the operator ð ‘… we prove that each Toeplitz operator 𠑇 ð ‘Ž with radial symbols is unitary to the multication operator ð ›¾ a , 𠜇 I . Meanwhile, the Wick function of a Toeplitz operator with radial symbol gives complete information about the operator, providing its spectral decomposition.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:210596

DOI: 10.1155/2011/210596

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