Hilbert-Schmidt Hankel operators with anti-holomorphic symbols on a class of unbounded complete Reinhardt domains

We consider a class of unbounded nonhyperbolic complete Reinhardt domains D-n,m,k(mu,p,s):={(z, w(1), . . . , w(m))is an element of C(n)xC(k1)x. . .xC(km):& Vert;w1 & Vert;(2p1)/ e(-mu 1 & Vert;z & Vert;s)+. . .+& Vert;w(m)& Vert;(2pm)/ e(-mu m & Vert;z & Vert;s)<1} wheres,p1, . . . , pm,mu 1, . . . , mu mare positive real numbers andn,k1, . . . , kmare positiveintegers. We show that if a Hankel operator with anti-holomorphic symbolis Hilbert-Schmidt on the Bergman space A(2)(D-n,m,k(mu,p,s)), then it must be zero. This gives an exampleof high dimensional unbounded complete Reinhardt domain that does not admit nonzeroHilbert-Schmidt Hankel operators with anti-holomorphic symbols