Spectral properties of the canonical solution operator to ¯∂

We study boundedness, compactness, and Schatten-class membership of the canonical solution operator to ¯∂, restricted to (0, 1)-forms with holomorphic coefficients, on L2(dμ) where μ is a measure with the property that the monomials form an orthogonal family in L2(dμ). The characterizations are formulated in terms of moment properties of μ. Our results generalize the results of the first author to several variables, contain some known results for several variables, and also cover new ground. © 2008 Elsevier Inc. All rights reserved.