Weighted Spaces of Analytic Functions on the Upper Half-Plane with Mixed Norm Defined in Terms of the Mellin Transform and Toeplitz Operators

On the upper half-plane, we introduce weighed mixed norm function spaces defined in terms of the Mellin transform. We describe the corresponding space of analytic functions and characterize the analytic functions in this space. In particular, we give an analog of the Paley–Wiener theorem. As an application, in these spaces of analytic functions we consider Toeplitz operators with symbols depending on the angular variable.