On the converse of the Shimorin--Pel\'aez--R\"atty\"a--Wick theorem

TL;DR

This paper provides necessary and sufficient conditions for a Shimorin kernel to correspond to a radial, logarithmically subharmonic weighted Bergman space, effectively establishing a converse to a known theorem.

Contribution

It introduces a converse to the Shimorin--Peláez--Rättyä--Wick theorem, characterizing kernels of specific weighted Bergman spaces.

Findings

Established necessary and sufficient conditions for Shimorin kernels.

Connected kernels to radial, logarithmically subharmonic weighted Bergman spaces.

Abstract

We establish a converse of the Shimorin--Pel\'{a}ez--R\"{a}tty\"{a}--Wick theorem. Specifically, we obtain necessary and sufficient conditions for a Shimorin kernel to be the kernel of a radial, logarithmically subharmonic weighted Bergman space.