Abstract
In this paper, we give a universal description of the boundedness and compactness of Toeplitz operator \({\cal T}_\mu ^\omega \) between Bergman spaces \(A_\eta ^p\) and \(A_\nu^q\) when μ is a positive Borel measure, 1 < p,q < ∞ and ω, η, ν are regular weights. By using Khinchin’s inequality and Kahane’s inequality, we get a new characterization of the Carleson measure for Bergman spaces induced by regular weights.
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The first author is supported by NNSF of China (Grant No. 12271328), Guangdong Basic and Applied Basic Research Foundation (Grant No. 2022A1515012117) and Projects of Talents Recruitment of GDUPT (Grant No. 2022rcyj2008) and the corresponding author is supported by STU Scientific Research Initiation Grant (Grant No. NTF23004)
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Du, J.T., Li, S.X. & Wulan, H. Toeplitz Operators and Carleson Measures for Weighted Bergman Spaces Induced by Regular Weights. Acta. Math. Sin.-English Ser. 40, 1345–1359 (2024). https://doi.org/10.1007/s10114-023-2396-z
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DOI: https://doi.org/10.1007/s10114-023-2396-z