Meromorphic Bergman spaces

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 Fejér-Riesz inequalities to these spaces with an application on Toeplitz operators.

15 pages, no figure