The Backward Shift on the Hardy Space

Contents......Page aa_0008_0001.djvu
Preface......Page aa_0010_0001.djvu
Numbering and notation......Page aa_0012_0001.djvu
Chapter 1. Overview......Page aa_0014_0001.djvu
2.1. Limits......Page aa_0022_0001.djvu
2.2. Pseudocontinuations......Page aa_0026_0001.djvu
3.2. H[sup(p)] and boundary values......Page aa_0030_0001.djvu
3.3. Fourier analysis and H[sup(p)] theory......Page aa_0034_0001.djvu
3.4. The Cauchy transform......Page aa_0036_0001.djvu
3.5. Duality......Page aa_0041_0001.djvu
3.6. The Nevanlinna class......Page aa_0052_0001.djvu
4.1. Motivation......Page aa_0058_0001.djvu
4.2. Basic definitions......Page aa_0060_0001.djvu
4.3. Poisson and conjugate Poisson integrals......Page aa_0062_0001.djvu
4.4. Maximal functions......Page aa_0065_0001.djvu
4.5. The Hilbert transform......Page aa_0067_0001.djvu
4.6. Some examples......Page aa_0068_0001.djvu
4.7. The harmonic Hardy space......Page aa_0073_0001.djvu
4.8. Distributions......Page aa_0074_0001.djvu
4.9. The atomic decomposition......Page aa_0085_0001.djvu
4.10. Distributions and H[sup(p)]......Page aa_0088_0001.djvu
4.11. The space H[sup(p)](C\R)......Page aa_0089_0001.djvu
5.1. The case p > 1......Page aa_0094_0001.djvu
5.2. The first and most straightforward proof......Page aa_0095_0001.djvu
5.3. The second proof - using Fatou's jump theorem......Page aa_0098_0001.djvu
5.4. Application: Bergman spaces......Page aa_0100_0001.djvu
5.5. Application: spectral properties......Page aa_0107_0001.djvu
5.6. The third proof - using the Nevanlinna theory......Page aa_0110_0001.djvu
5.7. Application: VMOA, BMOA, and L[sup(1)]/H[sup(1)][sub(0)]......Page aa_0112_0001.djvu
5.8. The case p = 1......Page aa_0114_0001.djvu
5.9. Cyclic vectors......Page aa_0118_0001.djvu
5.11. The commutant......Page aa_0122_0001.djvu
5.12. Compactness of the inclusion operator......Page aa_0124_0001.djvu
6.1. Introduction......Page aa_0128_0001.djvu
6.2. The parameters......Page aa_0133_0001.djvu
6.3. A reduction......Page aa_0146_0001.djvu
6.4. Rational approximation......Page aa_0149_0001.djvu
6.5. Spectral properties......Page aa_0198_0001.djvu
6.6. Cyclic vectors......Page aa_0199_0001.djvu
6.7. Duality......Page aa_0200_0001.djvu
6.8. The commutant......Page aa_0201_0001.djvu
Bibliography......Page aa_0204_0001.djvu
C......Page aa_0208_0001.djvu
H......Page aa_0209_0001.djvu
N......Page aa_0210_0001.djvu
S......Page aa_0211_0001.djvu
Z......Page aa_0212_0001.djvu