Real-Variable Methods in Harmonic Analysis (Google eBook)

Front Cover
Courier Dover Publications, Jul 12, 2012 - Mathematics - 480 pages
0 Reviews
"A very good choice." — MathSciNet, American Mathematical Society
An exploration of the unity of several areas in harmonic analysis, this self-contained text emphasizes real-variable methods. Appropriate for advanced undergraduate and graduate students, it starts with classical Fourier series and discusses summability, norm convergence, and conjugate function. An examination of the Hardy-Littlewood maximal function and the Calderón-Zygmund decomposition is followed by explorations of the Hilbert transform and properties of harmonic functions. Additional topics include the Littlewood-Paley theory, good lambda inequalities, atomic decomposition of Hardy spaces, Carleson measures, Cauchy integrals on Lipschitz curves, and boundary value problems. 1986 edition.
  

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Fourier Series 1 Fourier Series of Functions
1
Fourier Series of Continuous Functions
9
Elementary Properties of Fourier Series
13
Fourier Series of Functional
17
Notes Further Results and Problems
22
Cesara SammabUity 1 C 1 Summability
28
Fejérs Kernel
29
Characterization of Fourier Series of Functions and Measures
34
Subharmonic Functions 1
182
Harnacks and Mean Value Inequalities
187
Notes Further Results and Problems
191
Oscillation of Functions QQ 1 Mean Oscillation of Functions
199
The Maximal Operator and BMO
204
The Conjugate of Bounded and BMO Functions
206
WkL and A Interpolation
209
Lipschitz and Morrey Spaces
213

A E Convergence of C 1 Means of Summable Functions
41
Notes Further Results and Problems
43
Norm Convergence of Fourier Series 1 The Case LT Hilbert Space
48
Norm Convergence in LрT I p t
51
The Conjugate Mapping
52
More on Integrable Functions
54
Integral Representation of the Conjugate Operator
59
The Truncated Hilbert Transform
65
The Basic Principles 1 The CalderónZygmund Interval Decomposition
74
The HardyLittlewood Maximal Function
76
The CalderónZygmund Decomposition
84
The Marcinkiewicz Interpolation Theorem
87
Extrapolation and the Zygmund L In L Class 6 The Banach Continuity Principle and a e Convergence
97
Notes Further Results and Problems
109
The Hubert Transform and Multipliers 1 Existence of the Hilbert Transform of Integrable Functions
110
The Hübet i Transform in LT 1 p 3 Limiting Results
121
Multipliers 5 Notes Further Results and Problems 13
132
Paleys Theorem and Fractional Integration 1 Paleys Theorem
142
Fractional Integration
144
Multipliers
157
Notes Further Results and Problems
159
Harmonic and Subharmonic Functions 1 Abel Summability Nontangential Convergence
167
The Poisson and Conjugate Poisson Kernels
173
Harmonic Functions
176
Further Properties of Harmonic Functions
181
Notes Further Results and Problems
216
Measures
223
Ap Weights p 1
233
A and BMO
240
Notes Further Results and Problems
247
More about
259
The Hübet i and Riesz Transforms
266
CalderónZygmund Singular
280
CalderónZygmund Singular Integral Operators
286
Singular Integral Operators in IR
294
The LittlewoodPaley Theory
303
The LittlewoodPaley g Function
309
Hormanders Multiplier Theorem
319
The Good X Principle
328
Weighted Norm Inequalities for Maximal CZ Singular
330
Maximal Function Characterization of Hardy Spaces
350
Interpolation
363
Tent Spaces
381
Related Operators
408
Notes Further Results and Problems
416
Boundary Value Problems on CDomains
424
The Dirichlet and Neumann Problems
438
Index
457
Copyright

Common terms and phrases

Popular passages

Page 1 - Let X be a complete metric space and let Y* be a dual Banach space that is weak* 0--fragmented using weak* closed sets.
Page 1 - Let EI be a Banach space and let EI be a normed linear space. Furthermore, let {Tn} (n € N) be a family of bounded linear operators from E\ into...

References to this book

All Book Search results »

Bibliographic information