A Békollè–Bonami Class of Weights for Certain Pseudoconvex Domains

Dyadic Carleson embedding and sparse domination of weighted composition operators on strictly pseudoconvex domains

“…Dyadic decomposition on Ω. For this part, we mainly follow the framework built in [19,20,22]. Heuristically, the construction of a dyadic decomposition on Ω consists of two steps: I. bΩ is a space of homogeneous type, and hence it admits a dyadic decomposition; II.…”

“…We next make a remark about our choice of the domains. Recall that in [19], the pointwise for sparse bounds of the Bergman projection are actually valid when the domain Ω is a simple domain, which contains the smooth, bounded and strictly pseudoconvex domain as a particular case. We only consider strictly pseudoconvex domains here because we need the following off-diagonal estimate of the Bergman kernel function for (z, w) near the boundary diagonal:…”

A survey of the $$L^p$$ regularity of the Bergman projection

“…The estimates (2.3) are sometimes referred as the Bekollé-Bonami estimates. We also refer to [HWW20b,HWW20a] for a generalization on pseudoconvex domains. This chain of equivalences implies that smoothness of the conformal map F on the closure of the domains determines the regularity of the Bergman kernel and therefore also the estimates on the projection operator.…”

“…Furthermore, relate the operator norm of B Ω to the weight σ. Recently, [HWW20b] and [HWW20a] answered this question on some pseudoconvex domains on which sharp off-diagonal estimates on the Bergman kernel are known. They use a careful construction of dyadic decomposition on these domains by generalizing Carleson tents on the unit disc.…”

Weighted estimates for the Bergman projection on the Hartogs triangle

“…Later, Rahm, Tchoundja, and Wick [RTW17] generalized the results of Pott and Reguera to the unit ball case, and also obtained estimates for the Berezin transform. Sharp weighted norm estimates of the Bergman projection have been obtained [HW20] on the Hartogs triangle and a broad class of pseudoconvex domains [HWW20a,HWW20b,GHK20].…”