Fourier Analysis and Partial Differential Equations: (Studies in Advanced Mathematics)

Fourier Analysis and Partial Differential Equations presents the proceedings of the conference held at Miraflores de la Sierra in June 1992. These conferences are held periodically to assess new developments and results in the field. The proceedings are divided into two parts. Four mini-courses present a rich and actual piece of mathematics assuming minimal background from the audience and reaching the frontiers of present-day research. Twenty lectures cover a wide range of data in the fields of Fourier analysis and PDE. This book, representing the fourth conference in the series, is dedicated to the late mathematician Antoni Zygmund, who founded the Chicago School of Fourier Analysis, which had a notable influence in the development of the field and significantly contributed to the flourishing of Fourier analyis in Spain.

Table of Contents:
Introduction by the Editors: (J. García-Cuerva, E. Hernández, F. Soria, and J.-L. Torrea). Memorial Articles: Antoni Zygmund (G. Weiss). Stylianos Pichorides (J.-P. Kahane). Main Lectures: Band Limited Wavelets (A. Bonami, F. Soria, and G. Weiss). A Family of Degenerate Differential Operators (M. Christ). Solvability of Second Order PDOs on Nilpotent Groups - A Survey of Recent Results (D. Müller and F. Ricci). Recent Work on Sharp Estimates in Second Order Elliptic Unique Continuation Problems (T.H. Wolff). Contribution Articles: Weighted Lipschitz Spaces Defined by a Banach Space (O. Blasco). A Note on Monotone Functions (M.J. Carro and J. Soria). Hilbert Transforms in Weighted Distribution Spaces (C. Carton-Lebrun). Failure of an Endpoint Estimate for Integrals along Curves (M. Christ). Spline Wavelet Basis of Weighted Spaces (J. García-Cuerva and K.S. Kazarian). A Note on Hardy's Inequality in Orlicz Spaces (H. Heinig). A Characterization of Commutators of Parabolic Singular Integrals (S. Hofmann). Inequalities for Classical Operators in Orlicz Spaces (M. Krbec). On the Herz Spaces with Power Weights (S. Lu and F. Soria). On the One-Sided Hardy-Littlewood Maximal Function in the Real Line and in Dimensions Greater than One (F.J. Martin-Reyes). Characterization of the Besov Spaces (M. Paluszynski and M. Taibleson). Oscillatory Singular Integrals on Hardy Spaces (Y. Pan). Three Types of Weighted Inequalities for Integral Operators (L. Pick). Boundary Value Problems for Higher Order Operators in Lipschitz and C1 Domains (J. Pipher). Ap and Approach Regions (A. Sánchez-Colomer and J. Soria). Maximal Operators Associated to Hypersurfaces with One Nonvanishing Principal Curvature (C.D. Sogge).