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. Gutíerrez, E. Harboure, A.L. Karakhanyan, C.E. Kenig, R.A. Macías, J.J. Manfredi, F.J. Martín-Reyes, P. Ortega, R. Scotto, A. de la Torre, J.L. Torrea.

ANHA Series Preface Foreword Preface Publications of Carlos Segovia Carlos Segovia Fernández \ Roberto A. Mac¿ias and José L. Torrea Balls as Subspaces of Homogeneous Type: On a Construction due to R. Macías and C. Segovia \ Hugo Aimar Some Aspects of Vector-Valued Singular Integrals \ Oscar Blasco Products of Functions in Hardy and Lipschitz or BMO Spaces \ Aline Bonami and Justin Feuto Harmonic Analysis Related to Hermite Expansions \ Liliana Forzani, Eleonor Harboure, and Roberto Scotto Weights for One¿Sided Operators \ Francisco Javier Martín-Reyes, Pedro Ortega, and Alberto de la Torre Lectures on Gas Flow in Porous Media \ Luis A. Caffarelli and Aram L. Karakhanyan Sharp Global Bounds for the Hessian on Pseudo-Hermitian Manifolds \ Sagun Chanillo and Juan J. Manfredi Recent Progress on the Global Well-Posedness of the KPI Equation \ Carlos E. Kenig On Monge¿Ampère Type Equations and Applications \ Cristian E. Gutiérrez Index