Compact Toeplitz operators with unbounded symbols

We construct bounded Toeplitz operators on the Bergman space L-n(2) on the unit disk, whose symbols are unbounded functions. These opera- tors can be compact and in some cases Hilbert-Schmidt. In fact we show that for any (essentially unbounded) function H epsilon L-2 there is a set Gamma in the unit disk such that the (essentially unbounded) function given by h = chi(Gamma)H is the symbol for a compact Toeplitz operator on L-a(2).