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Sobolev Spaces in Mathematics II pp 31–68Cite as

Sobolev Spaces and their Relatives: Local Polynomial Approximation Approach

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Part of the book series: International Mathematical Series ((IMAT,volume 9))

Abstract

The paper presents a survey of the theory of local polynomial approximation and its applications to the study of the classical spaces of smooth functions. The study includes such topics as embeddings and extensions, pointwise differentiability and Luzin type theorems, nonlinear approximation by piecewise polynomials and splines, and the real interpolation.

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Authors and Affiliations

  1. Technion — Israel Institute of Technology, Haifa 32000, Israel

    Yuri Brudnyi

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  1. Yuri Brudnyi
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Correspondence to Yuri Brudnyi .

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Editors and Affiliations

  1. Department of Mathematics, Ohio State University, Columbus, USA

    Vladimir Maz'ya

  2. Department of Mathematical Sciences, University of Liverpool, Liverpool, UK

    Vladimir Maz'ya

  3. Department of Mathematics, Linköping University, Linköping, Sweden

    Vladimir Maz'ya

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Brudnyi, Y. (2009). Sobolev Spaces and their Relatives: Local Polynomial Approximation Approach. In: Maz'ya, V. (eds) Sobolev Spaces in Mathematics II. International Mathematical Series, vol 9. Springer, New York, NY. https://doi.org/10.1007/978-0-387-85650-6_4

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