Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe $overline{partial}$-equation on variable strictly pseudoconvex domains
130
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We investigate regularity properties of the $overline{partial}$-equation on domains in a complex euclidean space that depend on a parameter. Both the interior regularity and the regularity in the parameter are obtained for a continuous family of pseudoconvex domains. The boundary regularity and the regularity in the parameter are also obtained for smoothly bounded strongly pseudoconvex domains.
rate research
Read More
We construct a complete proper holomorphic embedding from any strictly pseudoconvex domain with $mathcal{C}^2$-boundary in $mathbb{C}^n$ into the unit ball of $mathbb{C}^N$, for $N$ large enough, thereby answering a question of Alarcon and Forstneric.
In this paper, we study the behavior of the weighted composition operators acting on Bergman spaces defined on strictly pseudoconvex domains via the sparse domination technique from harmonic analysis. As a byproduct, we also prove a weighted type estimate for the weighted composition operators which is adapted to Sawyer-testing conditions. Our results extend the work by the first author, Li, Shi and Wick under a much more general setting.
We obtain local estimates, also called propagation of smallness or Remez-type inequalities, for analytic functions in several variables. Using Carleman estimates, we obtain a three sphere-type inequality, where the outer two spheres can be any sets satisfying a boundary separation property, and the inner sphere can be any set of positive Lebesgue measure. We apply this local result to characterize the dominating sets for Bergman spaces on strongly pseudoconvex domains in terms of a density condition or a testing condition on the reproducing kernels. Our methods also yield a sufficient condition for arbitrary domains and lower-dimensional sets.
In this paper we introduce, via a Phragmen-Lindelof type theorem, a maximal plurisubharmonic function in a strongly pseudoconvex domain. We call such a function the {sl pluricomplex Poisson kernel} because it shares many properties with the classical Poisson kernel of the unit disc. In particular, we show that such a function is continuous, it is zero on the boundary except at one boundary point where it has a non-tangential simple pole, and reproduces pluriharmonic functions. We also use such a function to obtain a new intrinsic version of the classical Julias Lemma and Julia-Wolff-Caratheodory Theorem.
An extension of the estimates for the squeezing function of strictly pseudoconvex domains obtained recently by J. E. Fornae ss and E. Wold in cite{FW1} is applied to derive a sharp boundary behaviour of invariant metrics and Bergman curvatures.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
