Derivatives of the Berezin Transform. (29th February 2012) - Bommier-Hato, Hélène
Abstract : For a rotation invariant domainΩ, we considerA 2 ( Ω, μ ) the Bergman space and we investigate some properties of the rank one projectionA ( z ) : = 〈 ·, k z 〉 k z . We prove that the trace of all the strong derivatives of A ( z ) is zero. We also focus on the generalized Fock spaceA 2 ( μ m ), whereμ m is the measure with weighte - | z | m, m > 0, with respect to the Lebesgue measure onℂ n and establish estimations of derivatives of the Berezin transform of a bounded operator T onA 2 ( μ m ) .