Weighted Norm Inequalities and Related Topics, Issue 116

Front Cover
The unifying thread of this book is the topic of Weighted Norm Inequalities, but many other related topics are covered, including Hardy spaces, singular integrals, maximal operators, functions of bounded mean oscillation and vector valued inequalities. The emphasis is placed on basic ideas; problems are first treated in a simple context and only afterwards are further results examined.
 

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Contents

PREFACE vn CHAPTER I CLASSICAL THEORY OF HARDY SPACES
1
Harmonic functions Poisson representation
2
Subharmonic functions
26
F Riesz factorization theorem
39
Some classical inequalities
52
The conjugate function
59
H as a linear space
71
Canonical factorization theorem
78
Singular integral Operators
192
Multipliers
208
Notes and Further results
218
REAL VARIABLE THEORY OF HARDY SPACES
231
H spaces for the upper half plane
232
Maximal function characterizations of H
240
Atomic decompositions
247
h spaces in higher dimensions
273

The HelsonSzego theorem
84
The dual of H1
97
The corona theorem
117
Notes and Further results
125
CALDERONZYGMUND THEORY
133
The HardyLittlewood Maximal function and the Calderon Zygmund Decomposition
134
Norm estimates for the maximal function
144
The Sharp maximal function and the space B M O
155
Harmonic and subharmonic functions in a halfspace
167
Dual spaces
289
WEIGHTED NORM INEQUALITIES
385
VECTOR VALUED INEQUALITIES
475
FACTORIZATION THEOREMS AND WEIGHTED NORM INEQUALI
527
APPENDIX
581
REFERENCES
587
INDEX
601
Copyright

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