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.
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).
