Bounded Analytic Functions
by John B. Garnett · Springer (Graduate Texts in Mathematics 236)
Graduate text tying Hardy space theory to harmonic measure, BMO, Carleson measures and the Hilbert transform, then to interpolating sequences, Douglas algebras and Garnett's own account of the corona theorem, with substantial exercise sets.
This link may earn us a small commission at no extra cost to you. Affiliate disclosure
More resources on Hardy Spaces
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
Notes for Harmonic and Real Analysis (V4B5, Universität Bonn)
Complete lecture notes from a Bonn graduate course. Chapter 5 treats singular integrals of Calderón-Zygmund type, stating and proving the CZ theorem with worked examples; earlier chapters build the Hilbert transform, later ones cover Hardy spaces, BMO and Littlewood-Paley theory.
Linear Operators and Linear Systems: An Analytical Approach to Control Theory
The rigorous version of the control-engineering angle: it treats control as operator theory on Hardy spaces rather than as engineering recipes. Bridges Hardy space theory and control engineering: shift-invariant subspaces, Toeplitz and Hankel operators, the commutant lifting theorem and the gap metric, applied to stability, stabilization of linear systems, power signal spaces and delay systems.
Lecture Notes on Hardy Spaces (MA650)
A 111-page graduate course on Hardy spaces of the disc, working through Blaschke products, inner and outer functions, the factorization theorem, and Beurling's characterization of shift-invariant subspaces, with theorems proved rather than quoted.
Classical Spaces of Holomorphic Functions (lecture notes)
Fifty-six pages of University of Milan course notes building Hardy spaces on the unit disc — harmonic Hardy classes, Fatou's theorem, zero sets, boundary behaviour, the Cauchy-Szego projection — then Paley-Wiener theory and Hardy spaces on the upper half-plane.
Theory of H^p Spaces
Every other source on this topic cites Duren as the reference for the classical disc theory. The standard graduate reference on Hardy spaces of the unit disc: subharmonic functions, Blaschke products, inner-outer factorization, Taylor coefficients, interpolation theory, extremal problems and the corona theorem, with proofs worked in full detail.