Derivatives of the Berezin Transform

Abstract EN

For a rotation invariant domain Ω, we consider A2(Ω,μ) the Bergman space and we investigate some properties of the rank one projection A(z):=〈·,kz〉kz.

We prove that the trace of all the strong derivatives of A(z) is zero.

We also focus on the generalized Fock space A2(μm), where μm is the measure with weight e-|z|m, m>0, with respect to the Lebesgue measure on ℂn and establish estimations of derivatives of the Berezin transform of a bounded operator T on A2(μm).