The Bergman kernel function of some Reinhardt domains (II)

The boundary behavior of the Bergman kernel function of a kind of Reinhardt domain is studied. Upper and lower bounds for the Bergman kernel function are found at the diagonal points (Z, (Z) over bar). Let Omega be the Reinha rdt domain [GRAPHICS] where proportional to(j) > 0, j = 1,2,..., n, N = N-1 + N-2+ ...+ N-n, para llel to Z(j)parallel to is the standard Euclidean norm in C-N, J =1,2,, n; and let K(Z, (W) over bar) be the Bergman kernel function of Omega. Then th ere exist two 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 equ al to MF(Z,(Z) over bar) holds for every Z is an element of Omega. Here [GRAPHICS] and r(Z) = parallel to Z parallel to(alpha) - 1 is the defining function of Omega. The constants m and M depend only on alpha = (alpha(1), ... alpha(n )) and N-1, N-2, ... N-n, not on Z. This result extends some previous known results.