ON SOME CLASS OF INTEGRAL OPERATORS RELATED TO THE BERGMAN PROJECTION

We consider the integral operator C(alpha)f(z) = integral(D) f(xi)/(1 - z xi)(alpha) dA(xi), z epsilon D, where 0 < alpha < 2 and D is the unit disc in the complex plane. and investigate boundedness of it on the space L-p (D, d lambda), 1 < p < infinity, where d lambda is the Mbius invariant measure in D. We also consider the spectral properties of C-alpha when it acts on the Hilbert space L-2(D, d lambda), i.e., in the case p - 2, when C-alpha maps L-2 (D, d lambda) into the Dirichlet space.