Lipschitz estimates for the Berezin transform

Hélène Bommier-Hato
2010 Journal of Function Spaces and Applications  
We consider the generalized Fock spaceA2(μm), whereμmis the measure with weighte−|z|m,m > 0, with respect to the Lebesgue measure on Cn. Improving upon a recent result of L. Coburn and J. Xia, we show that for any bounded operatorXonA2(μm), the Berezin transform ofXsatisfies Lipschitz estimates.
doi:10.1155/2010/461315 fatcat:b6vigqqnzjdzje44ew7xh4sjii