Bergman spaces are a type of function space that consists of analytic functions defined on a domain, typically the unit disk in the complex plane. These functions are square-integrable with respect to a specific measure, known as the Bergman measure. This means that the integral of the square of the function's absolute value, multiplied by the measure, is finite. These spaces are named after the mathematician Bergman, who studied them in the context of complex analysis. They have applications in various fields, including operator theory and functional analysis, and are important for understanding the properties of analytic functions and their approximations.