Harmonic Analysis, Partial Differential Equations and Applications

This collection of articles and surveys is devoted to Harmonic Analysis, related Partial Differential Equations and Applications and in particular to the fields of research to which Richard L. Wheeden made profound contributions. The papers deal with Weighted Norm inequalities for classical operators like Singular integrals, fractional integrals and maximal functions that arise in Harmonic Analysis. Other papers deal with applications of Harmonic Analysis to Degenerate Elliptic equations, variational problems, Several Complex variables, Potential theory, free boundaries and boundary behavior of functions.

This book will be a collection of articles and surveys written by a very distinguished group of Mathematicians on an important field with far reaching consequences in other areas of Mathematics This volume will consist of articles that have connections to the work of Richard Wheeden who has made profound contributions to Fourier Analysis, and related applications to Partial Differential Equations This work is centered around the research interests of Richard L. Wheeden

Klappentext

This is a collection of contributed papers by many eminent Harmonic Analysts and specialists of Partial Differential equations. The papers focus on weighted norm equalities for singular integrals, focusing wave equations, degenerate elliptic equations, Navier-Stokes flow in two dimensions and Poincare-Sobolev inequalities in the setting of metric spaces equipped with measures among others. Many topics considered in this volume stem from the interests of Richard L. Wheeden whose contributions to Potential Theory, singular integral theory and degenerate elliptic PDE theory this volume honors. Luis Caffarelli, Sagun Chanillo, Bruno Franchi, Cristian Guttierez, Xiaojun Huang, Carlos Kenig, Ermanno Lanconelli, Eric Sawyer and Alexander Volberg, are some of the many contributors to this volume.

Inhalt

1. Introduction

2. Some new inequalities

3. A review of the extension property

4. Proofs of Theorem ?? and ??

5. Geometric Ambient Spaces

6. Appendix