Related papers: Reproducing kernel estimates, bounded projections …
Expected duality and approximation properties are shown to fail on Bergman spaces of domains in $\mathbb{C}^n$, via examples. When the domain admits an operator satisfying certain mapping properties, positive duality and approximation…
Let $M$ be a closed complex submanifold in ${\mathbb C}^N$ with the complete K\"ahler metric induced by the Euclidean metric. Several finiteness theorems on the $L^p$ Bergman space of holomorphic sections of a given Hermitian line bundle…
In this note we study some basic properties of general fractional derivatives induced by weighted Bergman kernels. As an application we demonstrate a method for generating pre-images of analytic functions under weighted Bergman projections.…
In this paper, we study the boundedness properties of the (dyadic) maximal bilinear operator associated with rough homogeneous kernels on $\mathbb{R}$. We establish sharp $L^{p_1}(\mathbb{R}) \times L^{p_2}(\mathbb{R}) \to…
The boundedness of $P_\omega:L^\infty(\mathbb{B})\to \mathcal{B}(\mathbb{B})$ and $P_\omega(P_\omega^+):L^p(\mathbb{B},\upsilon dV)\to L^p(\mathbb{B},\upsilon dV)$ on the unit ball of $\mathbb{C}^n$ with $p>1$ and $\omega,\upsilon\in…
We establish local asymptotic estimates of partial Bergman kernels on closed, $S^1$-symmetric K\"{a}hler manifolds. The main result concerns the scaling asymptotics of partial Bergman kernels at generic off-diagonal points in which they are…
We establish a global weighted $L^p$ estimate for the gradient of the solution to a divergence-form elliptic equations, where the coefficients are in a weighted VMO space and the equations have singularities on a co-dimension two boundary.
In this paper we investigate some properties of the harmonic Bergman spaces $\mathcal A^p(\sigma)$ on a $q$-homogeneous tree, where $q\geq 2$, $1\leq p<\infty$, and $\sigma$ is a finite measure on the tree with radial decreasing density,…
We shall give an explicit estimate of the lower bound of the Bergman kernel associated to a positive line bundle. In the compact Riemann surface case, our result can be seen as an explicit version of Tian's partial $C^0$-estimate.
It is shown that the property of being bounded below (having closed range) of weighted composition operators on Hardy and Bergman spaces can be tested by their action on a set of simple test functions, including reproducing kernels. The…
We compute explicitly the Bergman kernels of all two dimensional monomial polyhedra, a class of domains including the Hartogs triangle and some of its generalizations. The kernel is computed from the representation of such domains as…
We provide a counterexample to the Sarason Conjecture for the Bergman space and present a characterisation of bounded Toeplitz products on the Bergman space in terms of test functions by means of a dyadic model approach. We also present…
We derive necessary density conditions for sampling and for interpolation in general reproducing kernel Hilbert spaces satisfying some natural conditions on the geometry of the space and the reproducing kernel. If the volume of shells is…
The motivation of this paper comes from the two weight inequality $$\|P_\omega(f)\|_{L^p_v}\le C\|f\|_{L^p_v},\quad f\in L^p_v,$$ for the Bergman projection $P_\omega$ in the unit disc. We show that the boundedness of $P_\omega$ on $L^p_v$…
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 intersection of two complex ellipsoids $\{z \in \mathbb{C}^3 \colon |z_1|^p +…
This paper is devoted to the study of vector valued reproducing kernel Hilbert spaces. We focus on reproducing kernels in vector-valued reproducing kernel Hilbert spaces. In particular we extend reproducing kernels to relative reproducing…
We characterize those generating functions k that produce weighted Hardy spaces of the unit disk D supporting nontrivial Hermitian weighted composition operators. Our characterization shows that the spaces associated with the "classical…
In this paper, we study the norms of multiplication operators acting between weighted Bergman spaces. First, we provide a proof for a norm estimate previously announced in our recent paper \cite{Jin-c}. Second, we establish a sharp norm…
We establish weighted weak-type bounds for the Bergman projection with respect to Bekoll\'e-Bonami characteristics. We present two proofs of an improved quantitative weak-type $(1,1)$ estimate, as well as sharp weak-type $(p,p)$ bounds for…
In this paper we investigate a two classes of domains in $\mathbb{C}^n$ generalizing the Hartogs triangle. We prove optimal estimates for the mapping properties of the Bergman projection on these domains.