Meromorphic Bergman spaces

TL;DR

This paper introduces new generalized Bergman spaces of holomorphic functions on the unit disc, explores their properties and duals, and extends classical inequalities with applications to Toeplitz operators.

Contribution

It presents novel generalized Bergman spaces, analyzes their fundamental properties, and extends classical inequalities to these new spaces with practical operator applications.

Findings

New spaces of holomorphic functions generalizing classical Bergman spaces

Fundamental properties and dual spaces characterized

Extended Hardy-Littlewood and Fejér-Riesz inequalities with applications to Toeplitz operators

Abstract

In this paper we introduce new spaces of holomorphic functions on the pointed unit disc of $\mathbb C$ that generalize classical Bergman spaces. We prove some fundamental properties of these spaces and their dual spaces. We finish the paper by extending Hardy-Littlewood and Fej\'er-Riesz inequalities to these spaces with an application on Toeplitz operators.