Extension of \(A^ t\)-jets from holomorphic submanifolds (Q1319315)

Let \(D\) be a bounded strictly pseudoconvex domain of \(\mathbb{C}^ n\) with \({\mathcal C}^ \infty\) boundary and \(Y=\{z;u_ 1(z)=\cdots=u_ l(z)=0\}\) a holomorphic submanifold in a neighbourhood of \(\overline D\), of codimension \(l\) and transversal to the boundary of \(D\). The main objective of this work is to give necessary and sufficient conditions on a set of holomorphic functions \(\{f_ \alpha\}_{| \alpha | \leq m}\) on \(M=Y \cap D\), such that there exists a holomorphic Lipschitz function \(f\) on \(D\) such that \(D^ \alpha f |_ M=f_ \alpha\) for all \(| \alpha | \leq m\). To show this result we prove a theorem of resolution of the \(\overline \partial\)-equation in spaces of forms with coefficients with derivatives bounded for some powers of the distance at the boundary.