The canonical solution operator of $ {\bar \partial } $ on weighted spaces with holomorphic coefficients

Abstract

Key wordsOn weighted spaces with strictly plurisubharmonic weightfunctions the canonical solution operator of ∂ and the ∂-Neumann operator are bounded. In this paper we find a class of strictly plurisubharmonic weightfunctions with certain growth conditions, so that they are Hilbert-Schmidt operators between weighted spaces with different weightfunctions, if they are restricted to forms with holomorphic coefficients.