有界解析函数 英文版PDF电子书下载

Ⅰ．PRELIMINARIES 1

1．Schwarz's Lemma 1

2．Pick's Theorem 5

3．Poisson Integrals 10

4．Hardy-Littlewood Maximal Function 19

5．Nontangential Maximal Function and Fatou's Theorem 27

6．Subharmonic Functions 32

Notes 38

Exercises and Further Results 39

Ⅱ．HP SPACES 48

1．Definitions 48

2．Blaschke Products 51

3．Maximal Functions and Boundary Values 55

4．(1/π)∫(log|f(t)|/(1+t2))dt>-∞ 61

5．The Nevanlinna Class 66

6．Inner Functions 71

7．Beurling's Theorem 78

Notes 83

Exercises and Further Results 84

Ⅲ．CONJUGATE FUNCTIONS 98

1．Preliminaries 98

2．The LP Theorems 106

3．Conjugate Functions and Maximal Functions 111

Notes 118

Exercises and Further Results 120

Ⅳ．SOME EXTREMAL PROBLEMS 128

1．Dual Extremal Problems 128

2．The Carleson-Jacobs Theorem 134

3．The Helson-Szeg？ Theorem 139

4．Interpolating Functions of Constant Modulus 145

5．Parametrization of K 151

6．Nevanlinna's Proof 159

Notes 168

Exercises and Further Results 168

Ⅴ．SOME UNIFORM ALGEBRA 176

1．Maximal Ideal Spaces 176

2．Inner Functions 186

3．Analytic Discs in Fibers 191

4．Representing Measures and Orthogonal Measures 193

5．The Space L1/H 1 0 198

Notes 205

Exercises and Further Results 206

Ⅵ．BOUNDED MEAN OSCILLATION 215

1．Preliminaries 215

2．The John-Nirenberg Theorem 223

3．Littlewood-Paley Integrals and Carleson Measures 228

4．Fefferman's Duality Theorem 234

5．Vanishing Mean Oscillation 242

6．Weighted Norm Inequalities 245

Notes 259

Exercises and Further Results 261

Ⅶ．INTERPOLATING SEQUENCES 275

1．Carleson's Interpolation Theorem 275

2．The Linear Operator of Interpolation 285

3．Generations 289

4．Harmonic Interpolation 292

5．Earl's Elementary Proof 299

Notes 304

Exercises and Further Results 305

Ⅷ．THE CORONA CONSTRUCTION 309

1．Inhomogeneous Cauchy-Riemann Equations 309

2．The Corona Theorem 314

3．Two Theorems on Minimum Modulus 323

4．Interpolating Blaschke Products 327

5．Carleson's Construction 333

6．Gradients of Bounded Harmonic Functions 338

7．AConstructive Solution of ？b/？=μ 349

Notes 357

Exercises and Further Results 358

Ⅸ．DOUGLAS ALGEBRAS 364

1．The Douglas Problem 364

2．H∞+C 367

3．The Chang-Marshall Theorem 369

4．The Structure of Douglas Algebras 375

5．The Local Fatou Theorem and an Application 379

Notes 384

Exercises and Further Results 385

Ⅹ．INTERPOLATING SEQUENCES AND MAXIMAL IDEALS 391

1．Analytic Discs in ？ 391

2．Hoffman's Theorem 401

3．Approximate Dependence between Kernels 406

4．Interpolating Sequences and Harmonic Separation 412

5．A Constructive Douglas-Rudin Theorem 418

Notes 428

Exercises and Further Results 428

BIBLIOGRAPHY 434

INDEX 453