調和分析(2006年世界圖書出版公司出版圖書)

圖書目錄

PREFACE.

GUIDE TO THE READER

PROLOGUE

Ⅰ.REAL=VARIABLE THEORY

1.Basic assumptions

2.Examples

3.Covering lemmas and the maximal function

4.Generalization of the Calderdn-Zygmund decomposition

5.Singular integrals

6.Examples of the general theory

7.Appendix: Truncation of singular integrals

8.Further results

Ⅱ.MORE ABOUT MAXIMAL FUNCTIONS

1.Vector-valued maximal functions

2.Nontangential behavior and Carleson measures

3.Two applications

4.Singular approximations of the identity

5.Further results

Ⅲ.HARDY SPACES

1.Maximal characterization of Hp

2.Atomic decomposition for Hp

3.Singular integrals

4.Appendix:Relation with harmonic function

5.Further result

Ⅳ.H1 AND BMO

1.The space of functions of bounded mean oscillation

2.The sharp function

3.An elementary approach and a dyadic version

4.Further propeties of BMO

5.An interpolation theorem

6.Further results

Ⅴ.WEIGHTED INEQUALITIES

Ⅵ.PSEUDO-DIFFERENTIAL AND SINGULAR INTEGRAL OPERATORS：FOURIEV INTEGRAL