Grundlehren der mathematischen Wissenschaften

Function Spaces and Potential Theory

Authors: Adams, David R., Hedberg, Lars I.

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About this book

Function spaces, especially those spaces that have become known as Sobolev spaces, and their natural extensions, are now a central concept in analysis. In particular, they play a decisive role in the modem theory of partial differential equations (PDE). Potential theory, which grew out of the theory of the electrostatic or gravita­ tional potential, the Laplace equation, the Dirichlet problem, etc. , had a fundamen­ tal role in the development of functional analysis and the theory of Hilbert space. Later, potential theory was strongly influenced by functional analysis. More re­ cently, ideas from potential theory have enriched the theory of those more general function spaces that appear naturally in the study of nonlinear partial differential equations. This book is motivated by the latter development. The connection between potential theory and the theory of Hilbert spaces can be traced back to C. F. Gauss [181], who proved (with modem rigor supplied almost a century later by O. Frostman [158]) the existence of equilibrium potentials by minimizing a quadratic integral, the energy. This theme is pervasive in the work of such mathematicians as D. Hilbert, Ch. -J. de La Vallee Poussin, M. Riesz, O. Frostman, A. Beurling, and the connection was made particularly clear in the work of H. Cartan [97] in the 1940's. In the thesis of J. Deny [119], and in the subsequent work of J. Deny and J. L.

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"..carefully and thoughtfully written and prepared with, in my opinion, just the right amount of detail included...will certainly be a primary source that I shall turn to." Proceedings of the Edinburgh Mathematical Society

Table of contents (11 chapters)

  • Preliminaries

    Adams, David R. (et al.)

    Pages 1-16

  • Lp-Capacities and Nonlinear Potentials

    Adams, David R. (et al.)

    Pages 17-51

  • Estimates for Bessel and Riesz Potentials

    Adams, David R. (et al.)

    Pages 53-83

  • Besov Spaces and Lizorkin-Triebel Spaces

    Adams, David R. (et al.)

    Pages 85-127

  • Metric Properties of Capacities

    Adams, David R. (et al.)

    Pages 129-153

Buy this book

eBook $84.99
price for USA (gross)
  • ISBN 978-3-662-03282-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-540-57060-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • ISBN 978-3-642-08172-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Function Spaces and Potential Theory
Authors
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
314
Copyright
1996
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-03282-4
DOI
10.1007/978-3-662-03282-4
Hardcover ISBN
978-3-540-57060-8
Softcover ISBN
978-3-642-08172-9
Series ISSN
0072-7830
Edition Number
1
Number of Pages
XI, 368
Topics