Weighted Norm Inequalities and Related Topics

Weighted Norm Inequalities and Related Topics......Page 4
Copyright Page......Page 5
Contents......Page 10
Preface......Page 8
CHAPTER I. CLASSICAL THEORY OF HARDY SPACES......Page 12
1. Harmonic functions, Poisson representation......Page 13
2. Subharmonic functions......Page 37
3. F. Riesz factorization theorem......Page 50
4. Some classical inequalities......Page 63
5. The conjugate function......Page 70
6. HP as a linear space......Page 82
7. Canonical factorization theorem......Page 89
8. The Helson-Szegö theorem......Page 95
9. The dual of H1......Page 108
10. The corona theorem......Page 128
11. Notes and Further results......Page 136
CHAPTER II. CALDERON–ZYGMUND THEORY......Page 144
1. The Hardy-Littlewood Maximal function and the Calderon- Zygmund Decomposition......Page 145
2. Norm estimates for the maximal function......Page 155
3. The Sharp maximal function and the space B.M.O......Page 166
4. Harmonic and subharmonic functions in a half-space......Page 178
5. Singular integral Operators......Page 203
6. Multipliers......Page 219
7. Notes and Further results......Page 229
CHAPTER III. REAL VARIABLE THEORY OF HARDY SPACES......Page 242
1. Hp spaces for the upper half plane......Page 243
2. Maximal function characterizations of Hp......Page 251
3. Atomic decompositions......Page 258
4. Hp spaces in higher dimensions......Page 284
5. Dual spaces......Page 300
6. Interpolation of operators between Hp spaces......Page 318
7. Estimates for operators acting on Hp spaces......Page 326
8. Notes and Further results......Page 379
CHAPTER IV. WEIGHTED NORM INEQUALITIES......Page 396
1. The condition Ap......Page 398
2. The reverse Holder's inequality and the condition A∞......Page 406
3. Weighted norm inequalities for singular integrals......Page 422
4. Two-weight norm inequalities for maximal operators......Page 433
5. Factorization and extrapolation......Page 444
6. Weights in product spaces......Page 461
7. Notes and Further results......Page 475
1. Operators acting on vector valued functions: some basic facts......Page 486
2. A theorem of Marcinkiewicz and Zygmund......Page 493
3. Vector valued singular integrals......Page 502
4. Applications: Some maximal inequalities......Page 508
5. Applications: Some Littlewood-Paley theory......Page 515
6. Vector valued inequalities and Ap weights......Page 529
7. Notes and Further results......Page 533
CHAPTER VI. FACTORIZATION THEOREMS AND WEIGHTED NORM INEQUALITIES......Page 538
1. Factorization through weak-LP......Page 539
2. Nikishin's theorem......Page 544
3. Factorization through Lp......Page 553
4. Factorization of operators with values in Lq . The Dual Problem......Page 560
5. Weighted norm inequalities and vector valued inequalities......Page 566
6. The two weights problem for classical operators......Page 569
7. Weights of the form lxla for homogeneous operators......Page 577
8. Directional Hilbert transforms......Page 582
9. Notes and Further results......Page 588
A.1. Rademacher Functions......Page 592
A.2. The minimax lemma......Page 594
REFERENCES......Page 598
INDEX......Page 612