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Sobolev Embeddings and Hardy Operators

  • David E. Edmunds
  • W. Desmond Evans
Part of the International Mathematical Series book series (IMAT, volume 8)

Generalized ridged domains (GRD) are defined and examples of domains with irregular (even fractal) boundaries are given. Embedding problems on GRD are reduced to analogous problems on the generalized ridge (a tree in general). The latter problems involve Hardy type operators on trees with weights depending on geometric properties of the original GRD. Approximation and other singular numbers of Hardy type operators, including global bounds and asymptotic limits, are discussed.

Keywords

Approximation Number Sobolev Embedding Hardy Operator Hardy Type Entropy Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • David E. Edmunds
    • 1
  • W. Desmond Evans
    • 1
  1. 1.School of Mathematics Cardiff UniversityWalesUK

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