Morrey Spaces

Description

In this set of lecture notes, the author includes some of the latest research on the theory of Morrey Spaces associated with Harmonic Analysis.  There are three main claims concerning these spaces that are covered: determining the integrability classes of the trace of Riesz potentials of an arbitrary Morrey function; determining the dimensions of singular sets of weak solutions of PDE (e.g. The Meyers-Elcart System); and determining whether there are any “full” interpolation results for linear operators between Morrey spaces. This book will serve as a useful reference to graduate students and researchers interested in Potential Theory, Harmonic Analysis, PDE, and/or Morrey Space Theory.       Front Matter....Pages i-xvii Introduction....Pages 1-6 Function Spaces....Pages 7-12 Hausdorff Capacity....Pages 13-19 Choquet Integrals....Pages 21-27 Duality for Morrey Spaces....Pages 29-36 Maximal Operators and Morrey Spaces....Pages 37-42 Potential Operators on Morrey Spaces....Pages 43-50 Singular Integrals on Morrey Spaces....Pages 51-52 Morrey-Sobolev capacities....Pages 53-61 Traces of Morrey Potentials....Pages 63-69 Interpolation of Morrey Spaces....Pages 71-76 Commutators of Morrey Potentials....Pages 77-83 Mock Morrey Spaces....Pages 85-88 Morrey-Besov Spaces and Besov Capacity....Pages 89-93 Morrey Potentials and PDE I....Pages 95-102 Morrey Potentials and PDE II....Pages 103-109 Morrey Spaces On Complete Riemannian Manifolds....Pages 111-114 Back Matter....Pages 115-124