A collection of invited chapters dedicated to Carlos Segovia, this unified and self-contained volume examines recent developments in real and harmonic analysis. The work begins with a chronological description of Segovia's mathematical life, highlighting his original ideas and their evolution. Also included are surveys dealing with Carlos' favorite topics, and PDE works written by students and colleagues close to Segovia whose careers were in some way influenced by him. Contributors: H. Aimar, A. Bonami, O. Blasco, L.A. Caffarelli, S. Chanillo, J. Feuto, L. Forzani, C.E. Gutierrez, E. Harboure, A.L. Karakhanyan, C.E. Kenig, R.A. Macias, J.J. Manfredi, F.J. Martin-Reyes, P. Ortega, R. Scotto, A. de la Torre, J.L. Torrea.
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