Explicit traces of functions on Sobolev spaces and quasi-optimal linear interpolators

2012/11/07 by Daniel Estévez, Estévez, Daniel
Mathematics · #46E35 (Primary) 41A15 #58C25 (Secondary) #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration #math.CA #math.FA #msc:41A15 #msc:46E35 #msc:58C25

paper · pdf · doi:10.48550/arxiv.1211.1498

12 pages; 1 figure; Minor update regarding the dependence of constants on the parameter p

openalex publication_date 2012/11/07 · arxiv created 2014/01/20 · arxiv updated 2014/01/21 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

Let Λ⊂ R be a strictly increasing sequence. For r = 1,2, we give a simple explicit expression for an equivalent norm on the trace spaces W_p^r(R)|_Λ, L_p^r(R)|_Λ of the non-homogeneous and homogeneous Sobolev spaces with r derivatives W_p^r(R), L_p^r(R). We also construct an interpolating spline of low degree having optimal norm up to a constant factor. A general result relating interpolation in L^r_p(R) and W^r_p(R) for all r ≥ 1 is also given.

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