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

2012/10/01 by Pavel Shvartsman, Shvartsman, Pavel
Mathematics · #46E35 #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1210.0592

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

Abstract

Let p>n and let L¹_p(Rⁿ) be a homogeneous Sobolev space. For an arbitrary Borel measure μ on Rⁿ we give a constructive characterization of the space L¹_p(Rⁿ)+L_p(Rⁿ;μ). We express the norm in this space in terms of certain oscillations with respect to the measure μ. This enables us to describe the K-functional for the couple (L_p(Rⁿ;μ),L¹_p(Rⁿ)) in terms of these oscillations, and to prove that this couple is quasi-linearizable.

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