The Bergman kernel function of some Reinhardt domains

Abstract

The boundary behavior of the Bergman Kernel function of some Reinhardt domains is studied. Upper and lower bounds for the Bergman kernel function are found at the diagonal points (z,z~). Let D be the Reinhardt domain { ~ ~ ~~n} D z ~CnIlll 0, j = 1, 2,.. ., n; and let K(z, wi) be the Bergman kernel function of D. Then there exist two positive constants m and M and a function F such that mF(z, z) < K(z, z~) < MF(z, z) holds for every z E D. Here n F(z,z) = (-r(z))-n-1 J7J(-r(z) + lZj 12/C3)1-o j=1 and r(z) = JJzJJe1 is the defining function for D. The constants m and M depend only on ce = (cel, ., cen) and n, not on z.