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.
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.
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.
Innehållsförteckning
Carlos Segovia Fern#x00E1;ndez.- Balls as Subspaces of Homogeneous Type: On a Construction due to R. Mac#x00ED;as 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#x2013;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#x2013;Amp#x00E8;re Type Equations and Applications.
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