Related papers: Sobolev Regularity of the Bergman Projection on a …

Let $\Omega$ be a smooth bounded pseudoconvex domain in $\mathbb{C}^{n}$. It is shown that for $0\leq q\leq n$, $s\geq 0$, the embedding $j_{q}: dom(\overline{\partial})\cap dom(\overline{\partial}^{*}) \hookrightarrow…

Let $\Omega\subset\mathbb{C}^n$ be a bounded domain with smooth boundary, whose Bergman projection $B$ maps the Sobolev space $H^{k_{1}}(\Omega)$ (continuously) into $H^{k_{2}}(\Omega)$. We establish two smoothing results: (i) the full…

Generalizing a result of Berndtsson and Charpentier, we provide sufficient conditions for $L^2$ Sobolev regularity of the Bergman projection acting on $L^2$ sections of a holomorphic line bundle restricted to a relatively compact domain…

In this work we consider smooth unbounded worm domains $\mathcal Z_\lambda$ in $\mathbb C^2$ and show that the Bergman projection, densely defined on the Sobolev spaces $H^{s,p}(\mathcal Z_\lambda)$, $p\in(1,\infty)$, $s\ge0$, does not…

In this paper we investigate the regularity properties of weighted Bergman projections for smoothly bounded pseudo-convex domains of finite type in $\mathbb{C}^{n}$. The main result is obtained for weights equal to a non negative rational…

In this note we show that the weighted $L^{2}$-Sobolev estimates obtained by P. Charpentier, Y. Dupain & M. Mounkaila for the weighted Bergman projection of the Hilbert space $L^{2}\left(\Omega,d\mu_{0}\right)$ where $\Omega$ is a smoothly…

We prove precise growth and cancellation estimates for the Szeg\H{o} kernel of an unbounded model domain $\Omega\subset\mathbb{C}^2$ under the assumption that ${\rm b}\Omega$ satisfies a uniform finite-type hypothesis. Such domains have…

We obtain $L^p$ regularity for the Bergman projection on some Reinhardt domains. We start with a bounded initial domain $\Omega$ with some symmetry properties and generate successor domains in higher {dimensions}. We prove: If the Bergman…

Let $\Omega\subset \mathbb{C}^n$ be a smooth bounded pseudoconvex domain and $A^2 (\Omega)$ denote its Bergman space. Let $P:L^2(\Omega)\longrightarrow A^2(\Omega)$ be the Bergman projection. For a measurable $\varphi:\Omega\longrightarrow…

Let $D\subset\mathbb C^n$ be a bounded, strongly Levi-pseudoconvex domain with minimally smooth boundary. We prove $L^p(D)$-regularity for the Bergman projection $B$, and for the operator $|B|$ whose kernel is the absolute value of the…

In this new version, we give an affirmative solution to a conjecture of Cheng proposed in 1979 which asserts that the Bergman metric of a smoothly bounded strongly pseudoconvex domain in $\mathbb{C}^n, n\geq 2,$ is K\"ahler-Einstein if and…

We construct a bounded domain $\Omega$ in $\mathbb{C}^2$ with boundary of class $\mathcal{C}^{1,1}$, such that $\overline{\Omega}$ has a Stein neighborhood basis, but is not $s$-H-convex for any real number $s\geq{1}$.

The purpose of this paper is to prove that if a pseudoconvex domains $\Omega\subset\mathbb{C}^n$ satisfies Bell-Ligocka's Condition R and admits a ``good" dilation, then the Bergman projection has local $L^p$-Sobolev and H\"older estimates.…

Let $\Omega$ be a Stein space with a compact smooth strongly pseudoconvex boundary. We prove that the boundary is spherical if its Bergman metric over $\hbox{Reg}(\Omega)$ is K\"ahler-Einstein.

Let $\Omega$ be a smooth bounded pseudoconvex domain in $\mathbb{C}^{n}$. Let $1\leq q_{0}\leq (n-1)$. We show that if $q_{0}$--sums of eigenvalues of the Levi form are comparable, then if the Diederich--Forn\ae ss index of $\Omega$ is $1$,…

Consider a bounded, strongly pseudoconvex domain $D\subset \mathbb C^n$ with minimal smoothness (namely, the class $C^2$) and let $b$ be a locally integrable function on $D$. We characterize boundedness (resp., compactness) in $L^p(D), p >…

Let D be a smoothly bounded domain in a complex vector space of dimension n. Suppose that D has a smooth defining function, such that the sum of any q eigenvalues of its complex Hessian are non-negative on the closure of D. We show that…

Consider a Lipschitz domain $\Omega$ and a measurable function $\mu$ supported in $\overline\Omega$ with $\left\|{\mu}\right\|_{L^\infty}<1$. Then the derivatives of a quasiconformal solution of the Beltrami equation $\overline{\partial} f…

We prove the existence of a family of compact subdomains $\Omega$ of the flat cylinder $\mathbb{R}^N\times \mathbb{R}/2\pi\mathbb{Z}$ for which the Neumann eigenvalue problem for the Laplacian on $\Omega$ admits eigenfunctions with constant…

Consider a Lipschitz domain $\Omega$ and the Beurling transform of its characteristic function $\mathcal{B} \chi_\Omega(z)= - {\rm p.v.}\frac1{\pi z^2}*\chi_\Omega (z) $. It is shown that if the outward unit normal vector $N$ of the…