By Paul Koosis
The 1st version of this famous e-book used to be famous for its transparent and obtainable exposition of the elemental concept of Hardy areas from the concrete perspective (in the unit circle and the part plane). This moment variation keeps a few of the good points present in the first--detailed computation, an emphasis on methods--but tremendously extends its insurance. The discussions of conformal mapping now comprise Lindelöf's moment theorem and the only as a result of Kellogg. an easy derivation of the atomic decomposition for RH1 is given, after which used to supply another evidence of Fefferman's duality theorem. appendices via V.P. Havin have additionally been additional: on Peter Jones' interpolation formulation for RH1 and on Havin's personal facts of the susceptible sequential completeness of L1/H1(0). a variety of different additions, emendations and corrections were made all through.
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