Author | Bรถttcher, Albrecht. author |
---|---|
Title | Carleson Curves, Muckenhoupt Weights, and Toeplitz Operators [electronic resource] / by Albrecht Bรถttcher, Yuri I. Karlovich |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1997 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8922-3 |
Descript | XV, 400 p. online resource |
1 Carleson curves -- 1.1 Definitions and examples -- 1.2 Growth of the argument -- 1.3 Seifullayev bounds -- 1.4 Submultiplicative functions -- 1.5 The W transform -- 1.6 Spirality indices -- 1.7 Notes and comments -- 2 Muckenhoupt weights -- 2.1 Definitions -- 2.2 Power weights -- 2.3 The logarithm of a Muckenhoupt weight -- 2.4 Symmetric and periodic reproduction -- 2.5 Portions versus arcs -- 2.6 The maximal operator -- 2.7 The reverse Hรถlder inequality -- 2.8 Stability of Muckenhoupt weights -- 2.9 Muckenhoupt condition and W transform -- 2.10 Oscillating weights -- 2.11 Notes and comments -- 3 Interaction between curve and weight -- 3.1 Moduli of complex powers -- 3.2 U and V transforms -- 3.3 Muckenhoupt condition and U transform -- 3.4 Indicator set and U transform -- 3.5 Indicator functions -- 3.6 Indices of powerlikeness -- 3.7 Shape of the indicator functions -- 3.8 Indicator functions of prescribed shape -- 3.9 Notes and comments -- 4 Boundedness of the Cauchy singular integral -- 4.1 The Cauchy singular integral -- 4.2 Necessary conditions for boundedness -- 4.3 Special curves and weights -- 4.4 Brief survey of results on general curves and weights -- 4.5 Composing curves and weights -- 4.6 Notes and comments -- 5 Weighted norm inequalities -- 5.1 Again the maximal operator -- 5.2 The Calderรณn-Zygmund decomposition -- 5.3 Cotlarโs inequality -- 5.4 Good ? inequalities -- 5.5 Modified maximal operators -- 5.6 The maximal singular integral operator -- 5.7 Lipschitz curves -- 5.8 Measures in the plane -- 5.9 Cotlarโs inequality in the plane -- 5.10 Maximal singular integrals in the plane -- 5.11 Approximation by Lipschitz curves -- 5.12 Completing the puzzle -- 5.13 Notes and comments -- 6 General properties of Toeplitz operators -- 6.1 Smirnov classes -- 6.2 Weighted Hardy spaces -- 6.3 Fredholm operators -- 6.4 Toeplitz operators -- 6.5 Adjoints -- 6.6 Two basic theorems -- 6.7 Hankel operators -- 6.8 Continuous symbols -- 6.9 Classical Toeplitz matrices -- 6.10 Separation of discontinuities -- 6.11 Localization -- 6.12 Wiener-Hopf factorization -- 6.13 Notes and comments -- 7 Piecewise continuous symbols -- 7.1 Local representatives -- 7.2 Fredholm criterion -- 7.3 Leaves and essential spectrum -- 7.4 Metamorphosis of leaves -- 7.5 Logarithmic leaves -- 7.6 General leaves -- 7.7 Index and spectrum -- 7.8 Semi-Fredholmness -- 7.9 Notes and comments -- 8 Banach algebras -- 8.1 General theorems -- 8.2 Operators of local type -- 8.3 Algebras generated by idempotents -- 8.4 An N projections theorem -- 8.5 Algebras associated with Jordan curves -- 8.6 Notes and comments -- 9 Composed curves -- 9.1 Extending Carleson stars -- 9.2 Extending Muckenhoupt weights -- 9.3 Operators on flowers -- 9.4 Local algebras -- 9.5 Symbol calculus -- 9.6 Essential spectrum of the Cauchy singular integral -- 9.7 Notes and comments -- 10 Further results -- 10.1 Matrix case -- 10.2 Index formulas -- 10.3 Kernel and cokernel dimensions -- 10.4 Spectrum of the Cauchy singular integral -- 10.5 Orlicz spaces -- 10.6 Mellin techniques -- 10.7 Wiener-Hopf integral operators -- 10.8 Zero-order pseudodifferential operators -- 10.9 Conformal welding and Hasemanโs problem -- 10.10 Notes and comments