Estimates for functions in Sobolev spaces defined on unbounded domains
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- 作者：Ré ; mi Arcangé ; li ; Marí ; a Cruz Ló ; pez de Silanes ; Juan José ; Torrens
- 关键词：Sobolev bound ; Estimate ; Unbounded domain ; Affine-equivalence
- 刊名：Journal of Approximation Theory
- 出版年：2009
- 出版时间：November 2009
- 年：2009
- 卷：161
- 期：1
- 页码：198-212
- 全文大小：743 K
文摘
Given a function u belonging to a suitable Beppo–Levi or Sobolev space and an unbounded domain Ω in , we prove several Sobolev-type bounds involving the values of u on an infinite discrete subset A of Ω. These results improve the previous ones obtained by Madych and Potter [W.R. Madych, E.H. Potter, An estimate for multivariate interpolation, J. Approx. Theory 43 (1985) 132–139] and Madych [W.R. Madych, An estimate for multivariate interpolation II, J. Approx. Theory 142 (2006) 116–128].