Spectral properties of the canonical solution operator to dbar

Abstract

We study boundedness, compactness, and Schatten-class membership of the canonical solution operator to dbar, restricted to (0,1)-forms with holomorphic coefficients, on L^2(d mu) where mu is a measure with the property that the monomials form an orthogonal family in L^2 (d mu). The characterizations are formulated in terms of moment properties of mu. Our results generalize the results of the first author to several variables, contain some known results for several variables, and also cover new ground.