Embedding and fractional embedding of Bergman-type spaces in the Schatten class

Wenwan Yang, Xiao-Min Huang and Feifei Du

Applied Mathematics and Computation, 2024, vol. 472, issue C

Abstract: For 00. (2) For a positive Borel measure μ on Bm and a real number τ, we prove that the fractional embedding operator Iα+ττ:Aα2→L2(Bm,dμ) is in the Schatten p-class if and only if the Berezin transform of μ, denoted by μ˜αα+τ, is in Lp2(Bm,dλ), where dλ(z)=(1−|z|2)−m−1dv(z) is the Möbius invariant volume measure and dv is the Lebesgue measure on Bm, or equivalently, the averaging function of μ, denoted by μˆrα, is in Lp2(Bm,dλ).

Keywords: Weighted Bergman spaces; Embedding; Fractional embedding; Toeplitz operators; Schatten p-class (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:472:y:2024:i:c:s0096300324001000

DOI: 10.1016/j.amc.2024.128628

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