The -Neumann operator with Sobolev estimates up to a finite order

Abstract

Let be a bounded pseudoconvex domain with smooth boundary. For each we give a sufficient condition to estimate the -Neumann operator in the Sobolev space The key feature of our results is a precise formula for k in terms of the geometry of the boundary of Ω. It also shows the bound in the precise formula for Sobolev estimates of order k is comparably reciprocal of the Sobolev order k.