I'm an undergraduate mathematics student and I'm searching for notes and books on Hardy spaces $H^p$, in particular interpolation theory including topics like Carleson measures, Carleson's $H^\infty$ theorem on uniformly separated sequences, weighted interpolation in $H^p$, $p > 1$. The little knowledge that I have of Hardy spaces at this moment is restricted to stuff that is contained in the brief chapters 11 and 17 in Rudin's "Real and Complex Analysis".
My professor recommended
- Introduction to Hp Spaces, by Koosis
- Theory of Hp Spaces, by Duren
- Bounded Analytic Functions, by Garnett
All three books contain (some of or all) of the material I am after, and my background is (almost) sufficient to read them, but they are still pretty tough for me. I wonder if there are any other good texts/lecture notes which could help me.
You may find useful "Interpolation and Sampling in Spaces of Analytic Functions" by K. Seip (University Lecture Series of the AMS, vol 33). It talks about more spaces than the Hardy space, so Chapters I and II would be more than enough.
Anyway, Garnett is my favourite for a starter. In Garnett there are several proofs for some interpolation result. Try first the one called "Earl's elementary proof".