Sobolev $\frac{1}{2}$ estimates for $\overline{\partial }$ equations on strictly pseudoconvex domains with $C^2$ boundary

Abstract

We construct a solution operator for $\overline{\partial }$ equation that gains $\frac{1}{2}$ derivative in the fractional Sobolev space $H^{s,p}$ on bounded strictly pseudoconvex domains in ${\mathbb{C}}^n$ with $C^2$ boundary, for all $1<p<\infty$ and $s>\frac{1}{p}$.

31 pages