Carlos Segovia Fernández -- Balls as Subspaces of Homogeneous Type: On a Construction due to R. Macías and C. Segovia -- Some Aspects of Vector-Valued Singular Integrals -- Products of Functions in Hardy and Lipschitz or BMO Spaces -- Harmonic Analysis Related to Hermite Expansions -- Weights for One–Sided Operators -- Lectures on Gas Flow in Porous Media -- Sharp Global Bounds for the Hessian on Pseudo-Hermitian Manifolds -- Recent Progress on the Global Well-Posedness of the KPI Equation -- On Monge–Ampère Type Equations and Applications.

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, his original ideas and their evolution, which may be a source of inspiration for many mathematicians working in the fields of harmonic analysis, functional analysis, and partial differential equations. Apart from this contribution, two different types of chapters are featured in the work: 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. Specific topics covered include: * Vector-valued singular integral equations * Harmonic analysis related to Hermite expansions * Gas flow in porous media * Global well-posedness of the KPI Equation * Monge–Ampère type equations and applications * Spaces of homogeneous type * Hardy and Lipschitz spaces * One-sided operators This book will be useful to graduate students as well as pure and applied mathematicians interested in new mathematical developments in areas related to real and harmonic analysis. 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