調和分析

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

Ⅶ.PSEUDO-DIFFERENTIAL AND SINGULAR INTEGRAL

Ⅷ.OSCILLATORY INTEGRALS OF THE FIRST KIND

Ⅸ.OSCILLATORY INTEGRALS OF THE SECOND KING

Ⅹ.MAXIMAL OPERATORS：SOME EXAMPLES

Ⅺ.MAXIMAL AVERAGES AND OSCILLATORY INTEGRALS

Ⅻ.INTRODUCTION TO THE HEISENBERG GROUP

XIII.MORE ABOUT THE HEISENBERG GROUP

BIBLIOGRAPHY

AUTHOR INDEX

SUBJECT INDEX

Stein,E.M.，Stein在國際上享有盛譽，現任美國普林斯頓大學數學系教授，是當代分析，特別是調和分析領域領袖人物之一。1974年被選為美國國家科學院院士，1982年被選為美國文理學院院士，1984年獲美國數學會的Steele獎，1993年獲得瑞士科學院頒發的Schock獎，1999年獲得世 ^[1]  。