Morrey Spaces

1. Auflage 2015
ISBN: 978-3-319-26679-4
Verlag: Springer International Publishing

Buch, Englisch, 124 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 2292 g

Reihe: Lecture Notes in Applied and Numerical Harmonic Analysis

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.      

Zielgruppe

Research

Autoren/Hrsg.

Adams, David

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik

Inhaltsverzeichnis

Introduction.- Function Spaces.- Hausforff Capacity.- Choquet Integrals.- Duality for Morrey Spaces.- Maximal Operators and Morrey Spaces.- Potential Operators on Morrey Spaces.- Singular Integrals on Morrey Spaces.- Morrey-Sobolev Capacities.- Traces of Morrey Potentials.- Interpolation of Morrey Spaces.- Commutators of Morrey Potentials.- Mock Morrey Spaces.- Morrey-Besov Spaces and Besov Capacities.- Morrey Potentials and PDE I.- Morrey Potentials and PDE II.- Morrey Spaces on Complete Riemannian Manifolds.

Über Autor(innen)

David R. Adams is a Professor in the Department of Mathematics at the University of Kentucky. He received his Ph.D. from the University of Minnesota in 1969. His research areas include analysis and partial differential equations.