Sobolev spaces and Lagrange interpolation

2012/01/23 by Bogdan Bojarski, Bojarski, Bogdan · 1 citation
Engineering · Mathematics · #46E35 #Advanced Harmonic Analysis Research #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1201.4708

openalex publication_date 2012/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this short paper the discussion of the pointwise characterization of functions f in the Sobolev space W^m,p(\Rⁿ) given in the recent paper (Bojarski) is supplemented in \SS1 by a direct, essentially geometric, proof of the novel inequality (for m>1), appearing in Bojarski apparently for the first time, and involving the use of the m-th difference of the function f. Moreover in \SS2 some additional comments to the text in Bojarski are given and a natural class of Sobolev spaces in domains G in \Rⁿ is defined. \SS3 contains some final remarks.

Cited by

• Sobolev spaces and averaging I

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• Sobolev embeddings, extrapolations, and related inequalities
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• Sobolev spaces and averaging I
• Maximal inequalities for dual Sobolev spaces W^-1,p and applications to interpolation