A berndtsson-Andersson operator solving \bar\partial-equation with W^\alpha-estimates on convex domains of finite type

In this article, we use a Berndtsson-Andersson operator and the Bergman metric in order to solve the $\bar{\mathrm{\partial }}$ equation on convex domains of finite type for forms satisifying a Carleson condition and get norm estimates of the solution in term of the Carleson norm.