Abstract We study the Bergman metric of a finite ball quotient $\mathbb{B}^n/\Gamma $, where $n \geq 2$ and $\Gamma \subseteq{\operatorname{Aut}}({\mathbb{B}}^n)$ is finite, fixed point free, abelian group. prove that this Kähler–Einstein if only $ trivial, is, when unit ${\mathbb{B}}^n$ itself. As consequence, we characterize among normal Stein spaces with isolated singularities fundamental gr...

let $varphi(z)=z^m, z in mathbb{u}$, for some positive integer $m$, and $c_varphi$ be the composition operator on the bergman space $mathcal{a}^2$ induced by $varphi$. in this article, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators $c^*_varphi c_varphi, c_varphi c^*_varphi$ as well as self-commutator and anti-self-commutators of $c_...

Quaternionic analysis is a branch of classical referring to different generalizations the Cauchy-Riemann equations quaternion skew field \(\mathbb H\) context. In this work we deals with H-\)valued \((\theta , u)-\)hyperholomorphic functions related elements kernel Helmholtz operator parameter \(u \in \mathbb H\), just in same way as usual quaternionic set harmonic functions. Given domain \(\Om...

(Strictly speaking, one should put ( —1)"2/2 in front of £)'> but this is not essential in the following discussion.) Suppose F is ample in the following sense: (A.l). For every z in M, there exists an/ in F which does not vanish at 2. (A.2). For every holomorphic vector Z at z, there exists an/ in F such that / vanishes at z and Z(f *) ^0, where /=/ * dz1 A ■ ■ • Adzn with respect to a local c...

In this paper we study the complete invariant metrics on CartanHartogs domains which are the special types of Hua domains. Firstly, we introduce a class of new complete invariant metrics on these domains, and prove that these metrics are equivalent to the Bergman metric. Secondly, the Ricci curvatures under these new metrics are bounded from above and below by the negative constants. Thirdly, w...

In this paper, we characterize the boundedness and compactness of weighted composition operators ψCφf = ψfoφ acting between Bergman-type spaces.

We define positive Toeplitz operators between harmonic Bergman–Besov spaces $$b^p_\alpha $$ on the unit ball of $${\mathbb {R}}^n$$ for full ranges parameters $$0<p<\infty , $$\alpha \in {\mathbb {R}}$$ . give characterizations bounded and compact taking one space into another in terms Carleson vanishing measures. also a operator $$b^{2}_{\alpha }$$ to be Schatten class $$S_{p}$$ averaging func...

We study when a weighted composition operator acting between different weighted Bergman spaces is bounded, resp. compact.