On a Scale of Banach Spaces of Analytic Functions on a Convex Domain

The paper considers a family of Banach spaces of functions analytic in a bounded convex domain. In the first paragraph, a continuously parameterized family including the classical Smirnov and Bergman spaces is constructed. In the second section, based on this family, we construct a normal scale of Banach spaces, which also includes Smirnov and Bergman spaces. The authors suggest that the constructed scale will be an effective tool in the study of problems of approximation of analytical functions by exponentials.