Harmonic Analysis

Zusatztext "Elias M. Stein! Winner of the 1998 Wolf Prize for Mathematics! the Wolf Foundation" Informationen zum Autor Elias M. Stein is Professor of Mathematics at Princeton University. Klappentext 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(superscript p) estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group. Zusammenfassung Contains an exposition of some of the main developments 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, and relations of curvature to maximal inequalities. Inhaltsverzeichnis PrefaceGuide to the ReaderPrologue3IReal-Variable Theory7IIMore About Maximal Functions49IIIHardy Spaces87IVH[superscript 1] and BMO139VWeighted Inequalities193VIPseudo-Differential and Singular Integral Operators: Fourier Transform228VIIPseudo-Differential and Singular Integral Operators: Almost Orthogonality269VIIIOscillatory Integrals of the First Kind329IXOscillatory Integrals of the Second Kind375XMaximal Operators: Some Examples433XIMaximal Averages and Oscillatory Integrals467XIIIntroduction to the Heisenberg Group527XIIIMore About the Heisenberg Group587Bibliography645Author Index679Subject Index685

"Elias M. Stein, Winner of the 1998 Wolf Prize for Mathematics, the Wolf Foundation"

Autorentext
Elias M. Stein is Professor of Mathematics at Princeton University.

Klappentext
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(superscript p) estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group.

Zusammenfassung
Contains an exposition of some of the main developments 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, and relations of curvature to maximal inequalities.

Inhalt
PrefaceGuide to the ReaderPrologue3IReal-Variable Theory7IIMore About Maximal Functions49IIIHardy Spaces87IVH[superscript 1] and BMO139VWeighted Inequalities193VIPseudo-Differential and Singular Integral Operators: Fourier Transform228VIIPseudo-Differential and Singular Integral Operators: Almost Orthogonality269VIIIOscillatory Integrals of the First Kind329IXOscillatory Integrals of the Second Kind375XMaximal Operators: Some Examples433XIMaximal Averages and Oscillatory Integrals467XIIIntroduction to the Heisenberg Group527XIIIMore About the Heisenberg Group587Bibliography645Author Index679Subject Index685

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