Related papers: Bergman kernel and projection on the unbounded wor…

We study the off-diagonal decay of Bergman kernels $\Pi_{h^k}(z,w)$ and Berezin kernels $P_{h^k}(z,w)$ for ample invariant line bundles over compact toric projective \kahler manifolds of dimension $m$. When the metric is real analytic,…

The investigation of the dimension of Bergman spaces has long been a central topic in several complex variables, uncovering profound connections with potential theory and function theory since the pioneering work of Carleson, Wiegerinck,…

In this paper, we develop the theory of weighted Bergman space and obtain a general representation formula of the Bergman kernel function for the spaces on the Reinhardt domain containing the origin. As applications, we calculate the…

We study Bergman-Lorentz spaces on tube domains over symmetric cones, i.e. spaces of holomorphic functions which belong to Lorentz spaces $L(p, q).$ We establish boundedness and surjectivity of Bergman projectors from Lorentz spaces to the…

Given a sequence of positive Hermitian holomorphic line bundles $(L_p,h_p)$ on a K\"ahler manifold $X$, we establish the asymptotic expansion of the Bergman kernel of the space of global holomorphic sections of $L_p$, under a natural…

Let $\{\Omega_t:-1<t<1\}$ be a family of bounded pseudoconvex domains and $\varphi_t\in PSH(\Omega_t)$. Let $K_t(z,w)$ denote the Bergman kernel with weight $\varphi_t$ on $\Omega_t$. We study the continuity and H\"older continuity of…

We introduce the notion of "virtual Bergman kernel" and apply it to the computation of the Bergman kernel of "domains inflated by Hermitian balls", in particular when the base domain is a bounded symmetric domain.

In this paper, we investigate a class of domains $\Omega^{n+1}_\gamma =\{(z,w)\in \mathbb{C}^n\times \mathbb{C}: |z|^\gamma < |w| < 1\}$ for $\gamma>0$ that generalizes the Hartogs triangle. We obtain a sharp range of $p$ for the…

In this work we explore the theme of $L^p$-boundedness of Bergman projections of domains that can be covered, in the sense of ramified coverings, by "nice" domains (e.g. strictly pseudoconvex domains with real analytic boundary). In…

The boundary behavior of the Bergman metric near a convex boundary point $z_0$ of a pseudoconvex domain $D\subset\CC^n$ is studied; it turns out that the Bergman metric at points $z\in D$ in direction of a fixed vector $X_0\in\CC^n$ tends…

In this paper, we construct unbounded domains in $\C^n$ ($n\geq 2$), whose Bergman spaces are nontrivial and finite-dimensional. We further show that the Bergman metrics on these domains have positive constant sectional curvature equal to…

In this paper, we present an explicit description for the boundary behavior of the Bergman kernel function, the Bergman metric, and the associated curvatures along certain sequences converging to an $h$-extendible boundary point.

Our main result introduces a new way to characterize two-dimensional finite ball quotients by algebraicity of their Bergman kernels. This characterization is particular to dimension two and fails in higher dimensions, as is illustrated by a…

On a two dimensional Stein space with isolated, normal singularities, smooth finite type boundary, and locally algebraic Bergman kernel, we establish an estimate on the type of the boundary in terms of the local algebraic degree of the…

In this paper we obtain the closed forms of some hypergeometric functions. As an application, we obtain the explicit forms of the Bergman kernel functions for Reinhardt domains $\{|z_3|^{\lambda} < |z_1|^{2p} + |z_2|^2, \quad |z_1|^{2p} +…

In this paper we give an asymptotic expansion of the Bergman kernel for certain weakly pseudoconvex tube domains of finite type in C^2. Our asymptotic formula asserts that the singularity of the Bergman kernel at weakly pseudoconvex points…

In this paper, we first answer Chen-Zhang's problem on $p$-Bergman metric proposed in \cite{CZ22}. Second, we prove the off-diagonal p-Bergman kernel function $K_p(z,w)$ is H\"older continuous of order (1-$\varepsilon$) about the second…

We consider a bounded domain $\Omega \subseteq \mathbb C^d$ which is a $G$-space for a finite complex reflection group $G$. For each one-dimensional representation of the group $G,$ the relative invariant subspace of the weighted Bergman…

Let $\Omega\subset \mathbb{C}$ be an arbitrary domain in the one-dimensional complex plane equipped with a positive Radon measure $\mu$. For any $1\le p< \infty$, it is shown that the weighted Bergman space $A^p(\Omega, \mu)$ of holomorphic…

We develop the theory for the Bergman spaces of generalized $L_p$-solutions of the bicomplex-Vekua equation $\overline{\boldsymbol{\partial}}W=aW+b\overline{W}$ on bounded domains, where the coefficients $a$ and $b$ are bounded…