Related papers: Equivalent Bergman Spaces with Inequivalent Weight…
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…
In this article we prove that every germ of analytic meromorphic function at $(\mathbb{C}^{2},0)$ is equivalent, under the right composition by a germ of biholomorphism, to a germ of algebraic meromorphic function. An analogous result is…
We investigate problems related with the existence of square integrable holomorphic functions on (unbounded) balanced domains. In particular, we solve the problem of Wiegerinck for balanced domains in dimension two. We also give a…
In this paper, we study the Bergman kernel $B_\varphi(x,y)$ of generalized Bargmann-Fock spaces in the setting of Clifford algebra. The versions of $L^2$-estimate method and weighted subharmonic inequality for Clifford algebra are…
We study Sobolev spaces of radial functions on spherically symmetric Riemannian manifolds. Using geodesic polar coordinates, we give a sharp one-dimensional reduction: a radial function belongs to the Sobolev space on the manifold if and…
Relations between two classes of Hilbert spaces of entire functions, de Branges spaces and Fock-type spaces with non-radial weights, are studied. It is shown that any de Branges space can be realized as a Fock-type space with equivalent…
The paper provides weighted Sobolev inequalities of the Caffarelli-Kohn-Nirenberg type for functions with multi-radial symmetry. Similarly to the previously studied radial case, the range of parameters in CKN inequalities can be extended,…
In this paper, weighted Bergman spaces on the unit ball in C^n are investigated. A characterization of the Carleson embeddings is established. Pointwise and norm estimates on the reproducing kernel function of weighted Bergman spaces on the…
Let $A^p_\omega$ denote the Bergman space in the unit disc induced by a radial weight~$\omega$ with the doubling property $\int_{r}^1\omega(s)\,ds\le C\int_{\frac{1+r}{2}}^1\omega(s)\,ds$. The positive Borel measures such that the…
We give simple and unified proofs of weak holomorhpic Morse inequalities on complete manifolds, $q$-convex manifolds, pseudoconvex domains, weakly $1$-complete manifolds and covering manifolds. This paper is essentially based on the…
For any open hyperbolic Riemann surface $X$, the Bergman kernel $K$, the logarithmic capacity $c_{\beta}$, and the analytic capacity $c_{B}$ satisfy the inequality chain $\pi K \geq c^2_{\beta} \geq c^2_B$; moreover, equality holds at a…
We consider singular integrals associated to homogeneous kernels on self similar sets. Using ideas from ergodic theory we prove, among other things, that in Euclidean spaces the principal values of singular integrals associated to real…
There has been a great deal of work done in recent years on weighted Bergman spaces $\apa$ on the unit ball $\bn$ of $\cn$, where $0<p<\infty$ and $\alpha>-1$. We extend this study in a very natural way to the case where $\alpha$ is {\em…
We describe a notion of ampleness for line bundles on orbifolds with cyclic quotient singularities that is related to embeddings in weighted projective space, and prove a global asymptotic expansion for a weighted Bergman kernel associated…
We first prove a Cauchy's integral theorem and Cauchy type formula for certain inhomogeneous Cimmino system from quaternionic analysis perspective. The second part of the paper directs the attention towards some applications of the…
We study equivalence of invariant metrics on noncompact K\"ahler manifolds with a complete Bergman metric of bounded curvature. Especially only the boundedness of the ratio between Bergman kernel and the $n$-times wedge product of Bergman…
We prove that square integrable holomorphic functions (with respect to a plurisubharmonic weight) can be extended in a square integrable manner from certain singular hypersurfaces (which include uniformly flat, normal crossing divisors) to…
The theory of positive kernels and associated reproducing kernel Hilbert spaces, especially in the setting of holomorphic functions, has been an important tool for the last several decades in a number of areas of complex analysis and…
We prove a weighted version of the Hardy-Littlewood-Sobolev inequality for radially symmetric functions, and show that the range of admissible power weights appearing in the classical inequality due to Stein and Weiss can be improved in…
We introduce and study some new spaces of holomorphic functions on the right half-plane. In a previous work, S. Krantz, C. Stoppato and the first named author formulated the M"untz--Sz'asz problem for the Bergman space, that is, the problem…