Weighted Bergman kernels on orbifolds

A Remark on Weighted Bergman Kernels on Orbifolds

In this note, we explain that Ross–Thomas’ result [4, Theorem 1.7] on the weighted Bergman kernels on orbifolds can be directly deduced from our previous result [1]. This result plays an important role in the companion paper [5] to prove an orbifold version of Donaldson theorem. In two very interesting papers [4, 5], Ross–Thomas describe a notion of ampleness for line bundles on Kähler orbifold...

Weighted composition operators on weighted Bergman spaces and weighted Bloch spaces

In this paper, we characterize the bonudedness and compactness of weighted composition operators from weighted Bergman spaces to weighted Bloch spaces. Also, we investigate weighted composition operators on weighted Bergman spaces and extend the obtained results in the unit ball of $mathbb{C}^n$.

Toeplitz Operators and Weighted Bergman Kernels

For a smoothly bounded strictly pseudoconvex domain, we describe the boundary singularity of weighted Bergman kernels with respect to weights behaving like a power (possibly fractional) of a defining function, and, more generally, of the reproducing kernels of Sobolev spaces of holomorphic functions of any real order. This generalizes the classical result of Fefferman for the unweighted Bergman...

On Some Properties of Analytic Spaces Connected with Bergman Metric Ball

WEIGHTED BERGMAN KERNELS AND QUANTIZATIONMiroslav