Sobolev Extension By Linear Operators

2012/05/11 by Charles Fefferman, Fefferman, Charles L., Arie Israel +3 · 2 citations
Computer Science · Mathematics · #42B99 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1205.2525

openalex publication_date 2012/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let L^m,p(\Rⁿ) be the Sobolev space of functions with m^th derivatives lying in L^p(\Rⁿ). Assume that n< p < ∞. For E ⊂ \Rⁿ, let L^m,p(E) denote the space of restrictions to E of functions in L^m,p(\Rⁿ). We show that there exists a bounded linear map T : L^m,p(E) → L^m,p(\Rⁿ) such that, for any f ∈ L^m,p(E), we have Tf = f on E. We also give a formula for the order of magnitude of ‖f‖_L^m,p(E) for a given f : E → \R when E is finite.

Citations

• On The Sum Of A Sobolev Space And A Weighted L_P-Space

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