Morrey Spaces [electronic resource] / by David R. Adams.
Contributor(s): SpringerLink (Online service)Material type: TextSeries: Applied and Numerical Harmonic Analysis: Publisher: Cham : Springer International Publishing : Imprint: Birkhäuser, 2015Edition: 1st ed. 2015Description: XVII, 124 p. 1 illus. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783319266817Subject(s): Mathematics | Harmonic analysis | Functional analysis | Operator theory | Partial differential equations | Mathematics | Abstract Harmonic Analysis | Partial Differential Equations | Functional Analysis | Operator TheoryAdditional physical formats: Printed edition:: No titleDDC classification: 515.785 LOC classification: QA403-403.3Online resources: Click here to access online
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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.
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. .