scholarly journals ERRATUM to: Embeddings of Sobolev Spaces with Weights of Power Type

1986 ◽  
Vol 5 (5) ◽  
pp. 480-480
Author(s):  
David Edmunds ◽  
Alois Kufner ◽  
Jiří Rákosník
Keyword(s):  
Sobolev Spaces ◽  
Power Type ◽  
Sobolev Spaces With Weights

Embeddings of Sobolev Spaces with Weights of Power Type

1985 ◽  
Vol 4 (1) ◽  
pp. 25-34 ◽  
Author(s):  
David Edmunds ◽  
Alois Kufner ◽  
Jiří Rákosník
Keyword(s):  
Sobolev Spaces ◽  
Power Type ◽  
Sobolev Spaces With Weights

scholarly journals Analysis of the quadratic term in the backscattering transformation

2009 ◽  
Vol 105 (2) ◽  
pp. 218 ◽  
Author(s):  
Ingrid Beltita ◽  
Anders Melin
Keyword(s):  
Sobolev Spaces ◽  
Taylor Expansion ◽  
Bilinear Operator ◽  
Quadratic Term ◽  
Odd Dimensions ◽  
Sobolev Spaces With Weights

The quadratic term in the Taylor expansion at the origin of the backscattering transformation in odd dimensions $n\ge 3$ gives rise to a symmetric bilinear operator $B_2$ on $C_0^\infty({\mathsf R}^n)\times C_0^\infty({\mathsf R}^n)$. In this paper we prove that $B_2$ extends to certain Sobolev spaces with weights and show that it improves both regularity and decay.

Sobolev Spaces

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Sobolev Spaces ◽  
Embedding Theorems ◽  
Approximation Numbers ◽  
Selection Of

This chapter presents a selection of some of the most important results in the theory of Sobolev spacesn. Special emphasis is placed on embedding theorems and the question as to whether an embedding map is compact or not. Some results concerning the k-set contraction nature of certain embedding maps are given, for both bounded and unbounded space domains: also the approximation numbers of embedding maps are estimated and these estimates used to classify the embeddings.

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