THE BERGMAN-KERNEL FUNCTION OF SOME REINHARDT DOMAINS

The boundary behavior of the Bergman Kernel function of some Reinhardt domains is studied. Upper and lower bounds For the Bergman kernel fun ction are found at the diagonal points (z,(z) over bar). Let D be the Reinhardt domain [GRAPHICS] where a(j) > 0, j = 1,2,...,n; and let K(z ,(w) over bar) be the Bergman kernel function of D. Then there exist t wo positive constants m and M and a function F such that mF(z,(z) over bar) less than or equal to K(z,(z) over bar) less than or equal to MF (z,(z) over bar) holds for every z is an element of D. Here [GRAPHICS] and r(z) = \\z\\(alpha) - 1 is the defining function for D. The const ants m and M depend only on alpha = (alpha(1),...,alpha(n)) and n, not on z.