Carleson Curves, Muckenhoupt Weights, and Toeplitz OperatorsSpringer Science & Business Media, 1997 - Broj stranica: 397 Award-winning monograph of the Ferran Sunyer i Balaguer Prize 1997. This book is a self-contained exposition of the spectral theory of Toeplitz operators with piecewise continuous symbols and singular integral operators with piecewise continuous coefficients. It includes an introduction to Carleson curves, Muckenhoupt weights, weighted norm inequalities, local principles, Wiener-Hopf factorization, and Banach algebras generated by idempotents. Some basic phenomena in the field and the techniques for treating them came to be understood only in recent years and are comprehensively presented here for the first time. |
Sadržaj
Carleson curves | 1 |
12 Growth of the argument | 8 |
13 Seifullayev bounds | 11 |
14 Submultiplicative functions | 13 |
15 The W transform | 15 |
16 Spirality indices | 18 |
17 Notes and comments | 26 |
Muckenhoupt weights | 27 |
62 Weighted Hardy spaces | 207 |
63 Fredholm operators | 211 |
64 Toeplitz operators | 213 |
65 Adjoints | 215 |
66 Two basic theorems | 217 |
67 Hankel operators | 219 |
68 Continuous symbols | 221 |
69 Classical Toeplitz matrices | 222 |
22 Power weights | 30 |
23 The logarithm of a Muckenhoupt weight | 32 |
24 Symmetric and periodic reproduction | 35 |
25 Portions versus arcs | 39 |
26 The maximal operator | 44 |
27 The reverse Holder inequality | 48 |
28 Stability of Muckenhoupt weights | 56 |
29 Muckenhoupt condition and W transform | 59 |
210 Oscillating weights | 66 |
211 Notes and comments | 68 |
Interaction between curve and weight | 71 |
32 U and V transforms | 73 |
33 Muckenhoupt condition and U transform | 79 |
34 Indicator set and U transform | 84 |
35 Indicator functions | 90 |
36 Indices of powerlikeness | 97 |
37 Shape of the indicator functions | 101 |
38 Indicator functions of prescribed shape | 105 |
39 Notes and comments | 114 |
Boundedness of the Cauchy singular integral | 117 |
42 Necessary conditions for boundedness | 123 |
43 Special curves and weights | 130 |
44 Brief survey of results on general curves and weights | 137 |
45 Composing curves and weights | 139 |
46 Notes and comments | 144 |
Weighted norm inequalities | 145 |
52 The CalderonZygmund decomposition | 149 |
53 Cotlars inequality | 151 |
54 Good A inequalities | 157 |
55 Modified maximal operators | 160 |
56 The maximal singular integral operator | 165 |
57 Lipschitz curves | 171 |
58 Measures in the plane | 184 |
59 Cotlars inequality in the plane | 187 |
510 Maximal singular integrals in the plane | 190 |
511 Approximation by Lipschitz curves | 194 |
512 Completing the puzzle | 198 |
513 Notes and comments | 199 |
General properties of Toeplitz operators | 203 |
61 Smirnov classes | 204 |
610 Separation of discontinuities | 225 |
611 Localization | 226 |
612 WienerHopf factorization | 228 |
613 Notes and comments | 231 |
Piecewise continuous symbols | 235 |
72 Fredholm criterion | 240 |
73 Leaves and essential spectrum | 242 |
74 Metamorphosis of leaves | 243 |
75 Logarithmic leaves | 247 |
76 General leaves | 252 |
77 Index and spectrum | 258 |
78 SemiFredholmness | 261 |
79 Notes and comments | 265 |
Banach algebras | 267 |
82 Operators of local type | 270 |
83 Algebras generated by idempotents | 273 |
84 An N projections theorem | 275 |
85 Algebras associated with Jordan curves | 288 |
86 Notes and comments | 297 |
Composed curves | 301 |
92 Extending Muckenhoupt weights | 304 |
93 Operators on flowers | 316 |
94 Local algebras | 320 |
95 Symbol calculus | 326 |
96 Essential spectrum of the Cauchy singular integral | 329 |
97 Notes and comments | 330 |
Further results | 335 |
102 Index formulas | 338 |
103 Kernel and cokernel dimensions | 343 |
104 Spectrum of the Cauchy singular integral | 344 |
105 Orlicz spaces | 347 |
106 Mellin techniques | 353 |
107 WienerHopf integral operators | 365 |
108 Zeroorder pseudodifferential operators | 370 |
109 Conformal welding and Hasemans problem | 372 |
1010 Notes and comments | 377 |
Bibliography | 379 |
391 | |
Ostala izdanja - Prikaži sve
Carleson Curves, Muckenhoupt Weights, and Toeplitz Operators Albrecht Böttcher,Yuri I. Karlovich Ograničeni pregled - 2012 |
Carleson Curves, Muckenhoupt Weights, and Toeplitz Operators Albrecht Bottcher,Yuri I Karlovich Pregled nije dostupan - 1997 |