Derivatives of the Berezin Transform
Copyright policy )Derivatives of the Berezin Transform
For a rotation invariant domainΩ, we considerA2(Ω,μ)the Bergman space and we investigate some properties of the rank one projectionA(z):=〈⋅,kz〉kz. We prove that the trace of all the strong derivatives ofA(z) is zero. We also focus on the generalized Fock spaceA2(μm), whereμmis the measure with weighte-|z|m,m>0, with respect to the Lebesgue measure onℂnand establish estimations of derivatives of the Berezin transform of a bounded operatorTonA2(μm).
- Centrale Marseille France
- UNIVERSITE DE PROVENCE ( Aix-Marseille I ) France
- French National Centre for Scientific Research France
- UNIVERSITE DE PROVENCE France
- Aix-Marseille University France
Berezin transform, generalized Fock space, QA1-939, Bergman spaces of functions in several complex variables, Bergman space, [MATH] Mathematics [math], Hilbert spaces of continuous, differentiable or analytic functions, Mathematics
Berezin transform, generalized Fock space, QA1-939, Bergman spaces of functions in several complex variables, Bergman space, [MATH] Mathematics [math], Hilbert spaces of continuous, differentiable or analytic functions, Mathematics
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