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Harmonic Analysis
Real-Variable Methods, Orthogonality, and Oscillatory Integrals
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Elias M. Stein
Language:
English
Published/Copyright:
1993
About this book
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.
Author / Editor information
Elias M. Stein is Professor of Mathematics at Princeton University.
Reviews
"Elias M. Stein, Winner of the 1998 Wolf Prize for Mathematics, the Wolf Foundation"
"Elias M. Stein, Winner of the 2005 Stefan Bergman Prize, American Mathematical Society"
Topics
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Frontmatter
i -
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Contents
vii -
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Preface
xi -
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Guide to the Reader
xiii -
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Prologue
1 -
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I. Real-Variable Theory
7 -
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II. More about Maximal Functions
49 -
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III. Hardy Spaces
87 -
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IV. H1 and BMO
139 -
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V. Weighted Inequalities
193 -
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VI. Pseudo-Differential and Singular Integral Operators: Fourier Transform
228 -
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VII. Pseudo-Differential and Singular Integral Operators: Almost Orthogonality
269 -
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VIII. Oscillatory Integrals of the First Kind
329 -
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IX. Oscillatory Integrals of the Second Kind
375 -
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X. Maximal Operators: Some Examples
433 -
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XI. Maximal Averages and Oscillatory Integrals
467 -
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XII. Introduction to the Heisenberg Group
527 -
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XIII. More about the Heisenberg Group
587 -
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Bibliography
645 -
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Author Index
679 -
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Subject Index
685
Publishing information
Pages and Images/Illustrations in book
eBook published on:
June 2, 2016
eBook ISBN:
9781400883929
Pages and Images/Illustrations in book
Main content:
712
Other:
18 line illus.
eBook ISBN:
9781400883929
Keywords for this book
Singular integral; Theorem; Fourier transform; Heisenberg group; Maximal function; Oscillatory integral; Pseudo-differential operator; Cauchy–Riemann equations; Hilbert transform; Harmonic analysis; Support (mathematics); Submanifold; Special case; Fourier integral operator; Bounded mean oscillation; Dirac delta function; Projection (linear algebra); Harmonic function; Holomorphic function; Bounded operator; Orthogonality; Boundedness; Rectangle; Existential quantification; Hardy space; Lebesgue measure; Characterization (mathematics); Fourier analysis; Bessel function; Lie algebra; Marcinkiewicz interpolation theorem; Fundamental solution; Fubini's theorem; Variable (mathematics); Spectral theory; Locally integrable function; Commutator; Analytic function; Interpolation theorem; Convolution; Cauchy's integral theorem; Fourier inversion theorem; Hilbert space; Martingale (probability theory); Elliptic operator; Asymptotic formula; Square (algebra); Differential operator; Norm (mathematics); Riesz transform; Dirichlet problem; Laplace's equation; Fatou's theorem; Nilpotent Lie algebra; Translational symmetry; Boundary value problem; Function (mathematics); Poisson summation formula; Subharmonic function; Order of integration (calculus); Vector field; Meromorphic function; Gaussian curvature; Commutative property; Automorphism; Hölder's inequality; Characteristic polynomial; Banach space; Integral transform; Lipschitz continuity
Audience(s) for this book
College/higher education;Professional and scholarly;
