Lipschitz estimates for the Berezin transform

We consider the generalized fock space a 2(μ m),where μ m is the measure with weight e -|z|m,m > 0,with respect to the lebesgue measure on ℂ n. improving upon a recent result of l. coburn and j. xia,we show that for any bounded operator x on a 2(μ m),the berezin transform of x satisfies lipschitz estimates. copyright © 2010 hindawi publishing corporation.