L^p ‐estimates for the Bergman projection on strictly pseudoconvex nonsmooth domains

Abstract

We consider the Bergman projection on Henkin-Leiterer domains, bounded strictly pseudoconvex domains which have defining functions whose gradient is allowed to vanish. Our result describes the mapping properties of the Bergman projection between weighted L p spaces, with the weights being powers of the gradient of the defining function.

The Bergman projection on fat Hartogs triangles: $L^p$ boundedness

“…In all these cases, the Bergman projection is bounded on L p for all 1 < p < ∞. In two more recent works, [6] and [12], the Bergman projection is also shown to be bounded for the full range 1 < p < ∞ on some domains with less smooth boundary, but only for strongly pseudoconvex domains in this class.…”

$L^p$ estimates for the Bergman projection on some Reinhardt domains

“…In some cases, the Bergman projection is L p bounded for 1 < p < ∞, See [EL08,LS12]. For other domains, the projection has only a finite range of mapping regularity.…”

Sobolev regularity of the $$\overline{\partial }$$ -equation on the Hartogs triangle

“…In the context of non-smooth domains, it seems that singular weights are a natural device to control the behavior of functions and forms near the singular part of the boundary. Such weights also arise naturally in recent attempts to generalize classical estimates on the ∂ -and ∂ -Neumann problems from smooth to non-smooth strictly pseudoconvex domains (see [9,10,11]. )…”