Berezin transform and Toeplitz operators on weighted Bergman spaces induced by regular weights

2016/07/15 by Peláez, José Ángel, Rättyä, Jouni, Sierra, Kian
#Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1607.04394

Abstract

Given a regular weight ω and a positive Borel measure μ on the unit disc \mathbbD, the Toeplitz operator associated with μ is T_μ(f)(z)=∫_\mathbbD f(ζ)B_z^ω(ζ) dμ(ζ), where B^ω_z are the reproducing kernels of the weighted Bergman space A²_ω. We describe bounded and compact Toeplitz operators T_μ:A^p_ω→ A^q_ω, 1

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