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 B...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2024, Vol.45 (6), p.2688-2697
Main Authors: Isaev, K. P., Yulmukhametov, R. S.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Analytic functions
Banach spaces
Geometry
Mathematical analysis
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
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Summary: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.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080224602868