The Bergman projection and related integral operators on the unit ball in C(n)

This thesis deals with the question of the boundedness of the integral operators induced by Bergman type kernels. We prove that for any real numbers a, b, c, and b , where c is neither a negative integer nor zero, the integral operator Ta,b,cf z=1-z 2a B1-w 2b 1-&angl0;z,w&angr0;c fwduw is bounded on the space LpB,du b , 1 < p < infinity, where dubw =1-w2 bdu w and du is the normalized volume measure on the unit ball in Cn , if and only if -pa < b + 1 < p(b + 1) and c ≤ n + 1 + a + b. Furthermore we prove that for p = 1 the operator Ta,b,c is bounded on L1B,du b if and only if either -a < b + 1 ≤ b + 1 and c < n + 1 + a + b, or - a < b + 1 < b + 1 and c = n + 1 + a + b. If we let a = 0, b = alpha and c = n + 1 + alpha then we get the (weighted) Bergman projection Palpha = calpha T0,alpha,n+1+alpha . It is bounded on LpB,du b if and only if either 0 < b + 1 < p(alpha + 1).