Special Functions, Partial Differential Equations, and Harmonic Analysis

This volume of papers presented at the conference in honor of Calixto P. Calderón by his friends, colleagues, and students is intended to make the mathematical community aware of his important scholarly and research contributions in contemporary Harmonic Analysis and Mathematical Models applied to Biology and Medicine, and to stimulate further research in the future in this area of pure and applied mathematics.

Explores recent developments in the field and directions for future work Describes the history of the development of the Calderon-Zygmund school of harmonic analysis Draws out connections between different branches of the modern field of analysis Includes supplementary material: sn.pub/extras

Inhalt
Preface (Constantine Georgakis).- Remembrances and Silhouettes.- The Calderón brothers, a happy mathematical relation.- Calixto Calderón as I knew him.- An Appraisal of Calixto Calderón's Work in Mathematical Biology.- Remarks on various generalized derivatives.- Some non standard applications of the Laplace method.- Fejér Polynomials and Chaos.- A note on Widder's Inequality.- Solyanik Estimates in Harmonic Analysis.- Some open problems related with generalized Fourier series.- Modeling the Mechanics of Aneurysm Development and Rupture Computational Simulation of Aneurysm Evolution, Growth and Rupture.- Singular Integral Operators on C 1 Manifolds and C 1 Curvilinear Polygons.- Towards a unified theory of Sobolev inequalities.- Transference of fractional Laplacian regularity.- Local sharp maximal functions.- Weighted norm estimates for singular integrals with L log L kernels; Regularity of weak solutions of some degenerate quasilinear equations.