Related papers: Bergman projection induced by kernel with integral…

This monograph is devoted to the study of the weighted Bergman space $A^p_\om$ of the unit disc $\D$ that is induced by a radial continuous weight $\om$ satisfying {equation}\label{absteq} \lim_{r\to…

We show that any function in a Bergman space with exponential type weights admits a representation in terms of an infinite series of kernel functions.

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…

For doubling weights, we obtain a necessary and sufficient condition such that the one weighted inequality of the integral operator induced by Hardy kernels on the unit disk holds. This confirms a conjecture by Guo and Wang in such…

We study the $L^p$ regularity of the Bergman projection $P$ over the symmetrized polydisc in $\mathbb C^n$. We give a decomposition of the Bergman projection on the polydisc and obtain an operator equivalent to the Bergman projection over…

Let $U:[0,\infty)^2 \to [0,\infty)$ be a~measurable kernel satisfying: (i) $U(x,y)$ is nonincreasing in $x$ and nondecreasing in $y$; (ii) there exists a~constant $\theta>0$ such that $U(x,z) \le \theta\left( U(x,y)+U(y,z) \right)$ for all…

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…

We construct a bounded plane domain which is Bergman complete but for which the Bergman kernel does not tend to infinity as the point approaches the boundary.

Let L be an ample holomorphic line bundle over a compact complex Hermitian manifold X. Any fixed smooth Hermitian metric on L induces a Hilbert space structure on the space of global holomorphic sections with values in the k:th tensor power…

We study a family of strong fractional integral operators whose kernels have singularity on every coordinate subspace. We prove a desired two-weight, L^p-norm inequality provided that the corresponding multi-parameter theta-bump…

We give an extensive study on the Bergman kernel expansions and the random zeros associated with the high tensor powers of a semipositive line bundle on a complete punctured Riemann surface. We prove several results for the zeros of…

In this paper we study the diameter of Inhomogeneous random graphs $G(n,\kappa,p)$ that are induced by irreducible kernels $\kappa$. The kernels we consider act on separable metric spaces and are almost everywhere continuous. We generalize…

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.…

We establish the cancellation of the first |2j-q| terms in the diagonal asymptotic expansion of the restriction to the (0, 2j)-forms of the Bergman kernel associated to the modified spin^c Dirac operator on high tensor powers of a line…

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 >…

We consider mixed normed Bergman spaces on homogeneous Siegel domains. In the literature, two different approaches have been considered and several results seem difficult to be compared. In this paper we compare the results available in the…

We generalize the results of Montgomery for the Bochner Laplacian on high tensor powers of a line bundle. When specialized to Riemann surfaces, this leads to the Bergman kernel expansion and geometric quantization results for semi-positive…

In this paper we introduce and study a Bargmann-Radon transform on the real monogenic Bargmann module. This transform is defined as the projection of the real Bargmann module on the closed submodule of monogenic functions spanned by the…

We develop a new method that enables us to solve the open problem of characterizing discrete inequalities for kernel operators involving suprema. More precisely, we establish necessary and sufficient conditions under which there exists a…

This article establishes a bilinear embedding for second-order divergence-form operators with complex coefficients, characterized by the simultaneous presence of first-order terms and negative potentials. This work provides a further…