Essays On Fourier Analysis In Honor Of Elias M. Stein. (pms-42)

This volume of essays on Fourier analysis and its applications arose from a conference held at Princeton University in May 1991 in honour of the mathematician Elias Stein's 60th birthday. Topics discussed include oscillatory integrals, Hilbert transforms and nodal sets of eigenfunctions. This Book Contains The Lectures Presented At A Conference Held At Princeton University In May 1991 In Honor Of Elias M. Stein's Sixtieth Birthday. The Lectures Deal With Fourier Analysis And Its Applications. The Contributors To The Volume Are W. Beckner, A. Boggess, J. Bourgain, A. Carbery, M. Christ, R. R. Coifman, S. Dobyinsky, C. Fefferman, R. Fefferman, Y. Han, D. Jerison, P. W. Jones, C. Kenig, Y. Meyer, A. Nagel, D. H. Phong, J. Vance, S. Wainger, D. Watson, G. Weiss, V. Wickerhauser, And T. H. Wolff. The Topics Of The Lectures Are: Conformally Invariant Inequalities, Oscillatory Integrals, Analytic Hypoellipticity, Wavelets, The Work Of E. M. Stein, Elliptic Non-smooth Pde, Nodal Sets Of Eigenfunctions, Removable Sets For Sobolev Spaces In The Plane, Nonlinear Dispersive Equations, Bilinear Operators And Renormalization, Holomorphic Functions On Wedges, Singular Radon And Related Transforms, Hilbert Transforms And Maximal Functions On Curves, Besov And Related Function Spaces On Spaces Of Homogeneous Type, And Counterexamples With Harmonic Gradients In Euclidean Space. Introduction / Charles Fefferman, Robert Fefferman And Stephen Wainger -- 1. Selected Theorems By Eli Stein / Charles Fefferman -- 2. Geometric Inequalities In Fourier Analysis / William Beckner -- 3. Representing Measures For Holomorphic Functions On Type 2 Wedges / Al Boggess And Alexander Nagel -- 4. Some New Estimates On Oscillatory Integrals / Jean Bourgain -- 5. Dilations Associated To Flat Curves In R[superscript N] / Anthony Carbery, James Vance, Stephen Wainger And David Watson -- 6. Nonexistence Of Invariant Analytic Hypoelliptic Differential Operators On Nilpotent Groups Of Step Greater Than Two / Michael Christ -- 7. Operateurs Bilineaires Et Renormalisation / R. R. Coifman, S. Dobyinsky And Y. Meyer -- 8. Numerical Harmonic Analysis / R. R. Coifman, Y. Meyer And V. Wickerhauser -- 9. Some Topics From Harmonic Analysis And Partial Differential Equations / Robert A. Fefferman -- 10. Function Spaces On Spaces Of Homogeneous Type / Yongsheng Han And Guido Weiss -- 11. The First Nodal Set Of A Convex Domain / David Jerison -- 12. On Removable Sets For Sobolev Spaces In The Plane / Peter W. Jones -- 13. Oscillatory Integrals And Non-linear Dispersive Equations / Carlos E. Kenig -- 14. Singular Integrals And Fourier Integral Operators / D. H. Phong -- 15. Counterexamples With Harmonic Gradients In R[superscript 3] / Thomas H. Wolff. Edited By Charles Fefferman, Robert Fefferman, And Stephen Wainger. Proceedings Of The Princeton Conference In Harmonic Analysis, Held May 13-17, 1991. Includes Bibliographical References. This book contains the lectures presented at a conference held at Princeton University in May 1991 in honor of Elias M. Stein's sixtieth birthday. The lectures deal with Fourier analysis and its applications. The contributors to the volume are W. Beckner, A. Boggess, J. Bourgain, A. Carbery, M. Christ, R. R. Coifman, S. Dobyinsky, C. Fefferman, R. Fefferman, Y. Han, D. Jerison, P. W. Jones, C. Kenig, Y. Meyer, A. Nagel, D. H. Phong, J. Vance, S. Wainger, D. Watson, G. Weiss, V. Wickerhauser, and T. H. Wolff.The topics of the lectures are: conformally invariant inequalities, oscillatory integrals, analytic hypoellipticity, wavelets, the work of E. M. Stein, elliptic non-smooth PDE, nodal sets of eigenfunctions, removable sets for Sobolev spaces in the plane, nonlinear dispersive equations, bilinear operators and renormalization, holomorphic functions on wedges, singular Radon and related transforms, Hilbert transforms and maximal functions on curves, Besov and related function spaces on spaces of homogeneous type, and counterexamples with harmonic gradients in Euclidean space.Originally published in 1995.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.