Cocompact imbedding theorem for functions of bounded variation into Lorentz spaces

2021/12/04 by Lin Zhao, Zhao, Lin
Mathematics · #26B30 #46B50 #46E30 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:26B30 #msc:46B50 #msc:46E30

paper · pdf · doi:10.48550/arxiv.2112.02327

arxiv created 2021/12/04 · openalex publication_date 2021/12/04 · arxiv updated 2021/12/07 · openalex created_date 2021/12/31 · openalex updated_date 2026/07/28

Abstract

We show that the imbedding BV(ℝ^N)\hookrightarrow L^{1^∗,q}(ℝ^N), q>1 is cocompact with respect to group and the profile decomposition for BV(ℝ^N). This paper extends the cocompactness and profile decomposition for the critical space L^{1^∗}(ℝ^N) to Lorentz spaces L^{1^∗,q}(ℝ^N), q>1. A counterexample for BV(ℝ^N)\hookrightarrow L^{1^∗,1}(ℝ^N) not cocompact is given in the last section.

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