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Harmonic Analysis (PMS-43):
Real-Variable Methods, Orthogonality, and Oscillatory Integrals. (PMS-43)
Elias M. Stein

Elias M. Stein, Winner of the 2005 Stefan Bergman Prize, American Mathematical Society
Elias M. Stein, Winner of the 1998 Wolf Prize for Mathematics, the Wolf Foundation

Hardcover | 1993 | $150.00 | £124.95 | ISBN: 9780691032160
712 pp. | 6 x 9 1/4 | 18 line illus.
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This book contains an exposition of some of the main developments of the last twenty years in the following areas of harmonic analysis: singular integral and pseudo-differential operators, the theory of Hardy spaces, L\sup\ estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group.

Table of Contents:

Guide to the Reader
Prologue 3
I Real-Variable Theory 7
II More About Maximal Functions 49
III Hardy Spaces 87
IV H[superscript 1] and BMO 139
V Weighted Inequalities 193
VI Pseudo-Differential and Singular Integral Operators: Fourier Transform 228
VII Pseudo-Differential and Singular Integral Operators: Almost Orthogonality 269
VIII Oscillatory Integrals of the First Kind 329
IX Oscillatory Integrals of the Second Kind 375
X Maximal Operators: Some Examples 433
XI Maximal Averages and Oscillatory Integrals 467
XII Introduction to the Heisenberg Group 527
XIII More About the Heisenberg Group 587
Bibliography 645
Author Index 679
Subject Index 685

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