BERGMAN TYPE OPERATORS ON SOME GENERALIZED CARTAN-HARTOGS DOMAINS

For mu = (mu(1), ..., mu(t)) (mu(j) > 0), xi = (z(1), ..., z(t), w) is an element of C-n1 x ... x C-nt x C-m, define Omega(mu,t) = {xi is an element of B-n1 x ... x B-nt x C-m : parallel to w parallel to(2) < C(chi, mu) Pi(t)(j=1) (1-parallel to z(j)parallel to(2))(mu j)}, where B-nj is the unit ball in C-nj (1 <= j <= t), C(chi, mu) is a constant only depending on chi = (n(1), ..., n(t)) and mu = (mu(1), ..., mu(t)), which is a special type of generalized Cartan-Hartogs domain. We will give some sufficient and necessary conditions for the boundedness of some type of operators on L-p(Omega(mu, t), omega) (the weighted L-p space of Omega(mu, t) with weight omega, 1 < p < infinity). This result generalizes the works from certain classes of generalized complex ellipsoids to the generalized Cartan-Hartogs domain Omega(mu, t).