Includes bibliographical references (p. 191-194) and index.
CONTENTS NOTE
Text of Note
Classical boundary value results -- Limits -- Pseudocontinuations -- The Hardy space of the disk -- H[superscript p] and boundary values -- Fourier analysis and H[superscript p] theory -- The Cauchy transform -- Duality -- The Nevanlinna class -- The Hardy spaces of the upper-half plane -- Motivation -- Basic definitions -- Poisson and conjugate Poisson integrals -- Maximal functions -- The Hilbert transform -- Some examples -- The harmonic Hardy space -- Distributions -- The atomic decomposition -- Distributions and H[superscript p] -- The space H[superscript p] (C\R) -- The backward shift on H[superscript p] for p [set membership] (1, [infinity]) -- The case p ] 1 -- The first and most straightforward proof -- The second proof - using Fatou's jump theorem -- Application: Bergman spaces -- Application: spectral properties -- The third proof - using the Nevanlinna theory -- Application: VMOA, BMOA, and L[superscript 1] [square root]H[superscript 1 subscript 0] -- The case p = 1 -- Cyclic vectors -- Duality -- The commutant -- Compactness of the inclusion operator -- The backward shift on H[superscript p] for p [set membership] (0, 1) -- The parameters -- A reduction -- Rational approximation -- Spectral properties -- Cyclic vectors -- Duality -- The commutant.