Dyadic decomposition of convex domains of finite type and applications

Abstract

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

Refined Two Weight Estimates for the Bergman Projection

“…It is possible to construct a similar dyadic structure also on convex domains of finite type via the dyadic flow tents [GHK20]. This generalises the construction in §3 for the ball.…”