Morrey Spaces (Applied and Numerical Harmonic Analysis) by David Adams (PDF)

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.

User’s Reviews

Editorial Reviews: Review “This book gives a comparatively systematic discussion on the theory of Morrey spaces. … This book puts a lot of emphasis on the predual theory of the Morrey spaces as well as their applications. … the book has an impressive level of generality on the modern theory of Morrey spaces … . In addition, the related theories for Morrey spaces promise developments of this field in the near future.” (Liguang Liu, Mathematical Reviews, May, 2017)“This book contains the latest results obtained by the author. It is a useful reference to mathematicians working in potential theory, harmonic analysis and partial differential equations, in particular, in Morrey spaces theory.” (Sibei Yang, zbMATH 1339.42001, 2016) From the Back Cover 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. About the Author 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. Read more

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