Dyadic decomposition of convex domains of finite type and applications

In this paper, we introduce a dyadic structure on convex domains of finite type via the so-called flow tents. This allows us to establish weighted norm estimates for Bergman projection P such with respect Muckenhoupt weights. particular, result gives an alternative proof $$L^p$$ boundedness P. Moreover, using extrapolation, are also able derive vector-valued and modular inequalities projection.