| Abstrakt: |
Let \Omega be a strictly pseudoconvex domain in \mathbb {C}^n with C^{k+2} boundary, k \geq 1. We construct a \overline \partial solution operator (depending on k) that gains \frac 12 derivative in the Sobolev space H^{s,p} (\Omega) for any 1\frac {1}{p} -k. If the domain is C^{\infty }, then there exists a \overline \partial solution operator that gains \frac 12 derivative in H^{s,p}(\Omega) for all s \in \mathbb {R}. We obtain our solution operators via the method of homotopy formula. A novel technique is the construction of "anti-derivative operators" for distributions defined on bounded Lipschitz domains. [ABSTRACT FROM AUTHOR] |
