Hardy spaces

Hardy spaces are a class of mathematical spaces used to analyze complex functions, particularly those that are analytic (smooth and differentiable) inside a domain like the unit disk or upper half-plane. They focus on functions with controlled growth near the boundary, making them useful in fields like signal processing, control theory, and complex analysis. Essentially, Hardy spaces organize functions based on how their "size" (measured by integrals) behaves approaching the boundary, allowing mathematicians to study properties like boundary behavior and harmonic extensions with precision.