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- W4298270212 abstract "Given a regular weight $omega$ and a positive Borel measure $mu$ on the unit disc $mathbb{D}$, the Toeplitz operator associated with $mu$ is $$ mathcal{T}_mu(f)(z)=int_{mathbb{D}} f(zeta)bar{B_z^omega(zeta)},dmu(zeta), $$ where $B^omega_{z}$ are the reproducing kernels of the weighted Bergman space $A^2_omega$. We describe bounded and compact Toeplitz operators $mathcal{T}_mu:A^p_omegato A^q_omega$, $1<q,p<infty$, in terms of Carleson measures and the Berezin transform $$ widetilde{mathcal{T}_mu}(z)=frac{langlemathcal{T}_mu(B^omega_{z}), B^omega_{z} rangle_{A^2_omega}}{|B_z^omega|^2_{A^2_omega}}. $$ We also characterize Schatten class Toeplitz operators in terms of the Berezin transform and apply this result to study Schatten class composition operators." @default.
- W4298270212 created "2022-10-01" @default.
- W4298270212 creator A5029327211 @default.
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- W4298270212 date "2016-07-15" @default.
- W4298270212 modified "2023-09-26" @default.
- W4298270212 title "Berezin transform and Toeplitz operators on weighted Bergman spaces induced by regular weights" @default.
- W4298270212 doi "https://doi.org/10.48550/arxiv.1607.04394" @default.
- W4298270212 hasPublicationYear "2016" @default.
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