Compact Hankel Operators on Generalized Bergman Spaces of the Polydisc

Let v be a measure on the polydisc D(n) which is the product of n regular Borel probability measures so that v([ r, 1)(n) x T(n)) > 0 for all 0 < r < 1. The Bergman space A(v)(2) consists of all holomorphic functions that are square integrable with respect to.. In one dimension, it is well known that if f is continuous on the closed disc (D) over bar, then the Hankel operator H(f) is compact on A(v)(2). In this paper we show that for n >= 2 and f a continuous function on (D) over bar (n), H(f) is compact on A(v)(2). if and only if there is a decomposition f = h + g, where h belongs to A(v)(2). and lim(z ->partial derivative D)(n) g(z) = 0.