A \(q\)-analogue of the weighted Bergman space on the disk and associated second \(q\)-Bargmann transform (Q302089)

Using Jackson's \(q\)-integration, \(0<q<1\), the authors introduce a \(q\)-analogue of the classical Bergman space on the unit disk of \(\mathbb{C}\). They give an explicit expression for the corresponding reproducing kernel and investigate a \(q\)-analog of the second Bargmann integral transform.