Compactness of Solution of - Neumann Operator in Weighted L2 – Spaces

Abstract

We consider the space of square integrable functions with respect to a measure on a rotation invariant open set. We give necessary and sufficient conditions, in terms of the moments of the measure, for the con canonical solution operator of the -equation, to be bounded and compact - we give a sufficient condition for subelliptic estimates for the - Neumann operator on smoothly bounded pseudo convex domains on the unitary space. We also discuss compactness of the -canonical solution operator on weighted L2 spaces. Finally, we show the spectral properties of the -canonical solution operator.