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Tables of Contents for Haar Series and Linear Operators
Chapter/Section Title
Page #
Page Count
Preface
vii
2
Acknowledgements
ix
2
Remarks
xi
 
Chapter 1. Preliminaries
1
14
1.a. Measure space
1
1
1.b. Main results on bases in Banach spaces
1
3
1.c. Rearrangements of Functions
4
1
1.d. Rearrangement in invariant spaces
5
5
1.e. Interpolation methods
10
5
Chapter 2. Definition and Main Properties of the Haar System
15
4
Chapter 3. Convergence of Haar Series
19
6
Chapter 4. Basis Properties of the Haar System
25
8
4.a. R.i. spaces
25
3
4.b. Spaces Lp(w)
28
5
Chapter 5. The Unconditionality of the Haar System
33
8
Chapter 6. The Paley Function
41
10
Chapter 7. Fourier-Haar Coefficients
51
22
7.a. The spaces Lp and r.i. spaces
51
13
7.b. Absolutely continuous functions
64
3
7.c. Continuous functions
67
4
7.d. Characteristic functions
71
2
Chapter 8. The Haar System and Martingales
73
10
Chapter 9. Reproducibility of the Haar System
83
6
Chapter 10. Generalized Haar Systems and Monotone Bases
89
20
10.a. D-convexity and C-concavity of r.i. spaces
89
8
10.b. Generalized Haar systems
97
12
Chapter 11. Haar System Rearrangements
109
18
Chapter 12. Fourier-Haar Multipliers
127
6
Chapter 13. Pointwise Estimates of Multipliers
133
10
Chapter 14. Estimates of Multipliers in L1
143
8
Chapter 15. Subsequences of the Haar System
151
18
Chapter 16. Criterion of Equivalence of the Haar and Franklin Systems in R.I. Spaces
169
22
16.a. Definition and basic properties of the Franklin System
169
1
16.b. Martingale transforms of the Haar functions
170
7
16.c. Norm estimates of auxiliary operators
177
5
16.d. Equivalence of the Haar and the Franklin system in Lp 1[p]
182
2
16.e. The Haar and the Franklin systems in r.i. spaces with trival Boyd indeces
184
7
Chapter 17. Olevskii Systems
191
4
References
195