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 analysis in Spain.
Table of Contents
1. Antoni Zygmund 2. Stylianos Pichorides. Main Lectures 3. Band Limited Wavelets 4. A Family of Degenerate Differential Operators 5. Solvability of Second Order PDOs on Nilpotent Groups - A Survey of Recent Results 6. Recent Work on Sharp Estimates in Second Order Elliptic Unique Continuation Problems. Contribution Articles 7. Weighted Lipschitz Spaces Defined by a Banach Space 8. A Note on Monotone Functions 9. Hilbert Transforms in Weighted Distribution Spaces 10. Failure of an Endpoint Estimate for Integrals along Curves 11. Spline Wavelet Basis of Weighted Spaces 12. A Note on Hardy's Inequality in Orlicz Spaces 13. A Characterization of Commutators of Parabolic Singular Integrals 14. Inequalities for Classical Operators in Orlicz Spaces 15. On the Herz Spaces with Power Weights 16. On the One-Sided Hardy-Littlewood Maximal Function in the Real Line and in Dimensions Greater than One 17. Characterization of the Besov Spaces 18. Oscillatory Singular Integrals on Hardy Spaces 19. Three Types of Weighted Inequalities for Integral Operators 20. Boundary Value Problems for Higher Order Operators in Lipschitz and C1 Domains 21. Ap and Approach Regions 22. Maximal Operators Associated to Hypersurfaces with One Nonvanishing Principal Curvature.