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| Stein,E.M.，Stein在国际上享有盛誉，现任美国普林斯顿大学数学系教授，是当代分析，特别是调和分析领域领袖人物之一。1974年被选为美国国家科学院院士，1982年被选为美国文理学院院士，1984年获美国数学会的Steele奖，1993年获得瑞士科学院颁发的Schock奖，1999年获得世界性Wolf数学奖。 |
| 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 |
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