Theory of Hp Spaces
A blend of classical and modern techniques and viewpoints, this text examines harmonic and subharmonic functions, the basic structure of Hp functions, applications, conjugate functions, and mean growth and smoothness. Other subjects include Taylor coefficients, Hp as a linear space, interpolation theory, the corona theorem, and more. Information on Rademacher functions and maximal theorems appears in the appendixes. Essentially self-contained, with a list of exercises in each chapter, this text is appropriate for researchers or second- or third-year graduate students. 1970 edition.
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HARMON1C AND SUBHARMON1C FUNCT1ONS
z BAS1C STRUCTURE OF H FUNCT1ONS
MEAN GROWTH AND SMOOTHNESS
Ht AS A L1NEAR SPACE
U SPACES OVER GENERAL DOMA1NS
absolutely continuous Amer analytic functions applied arbitrary Bergman spaces Blaschke product Bloch space BMOA boundary function bounded linear functional bounded variation Carleson measure Cauchy integral Chapter coefficients conformal mapping conjugate connected domains constant Conversely convex COROLLARY corona theorem defined Duren exists extremal function extremal kernel extremal problem extreme point factorization theorem Fatou's lemma follows Fourier function of bounded Hardy and Littlewood Hardy spaces harmonic function harmonic majorant Hence Hp functions Hp spaces Hp(D implies inequality Jordan curve Jordan domain lemma ln fact ln particular multipliers nondecreasing norm outer function Poisson integral polynomials Proc proof of Theorem proved radial limit rectifiable boundary result Riesz theorem Section sequence set of positive Shapiro singular inner function Smirnov domain subharmonic subspace suppose Theorem 3.1 theory uniformly separated unique unit circle unit disk vanish Zygmund
Page 259 - Schwarz's lemma and the Szegö kernel function. Trans. Amer. Math. Soc. 67 (1949), 1-35. Gaudry, G. l.  Я' multipliers and inequalities of Hardy and Littlewood.