On grand Sobolev spaces and pointwise description of Banach function\n spaces

2020/04/27 by Pankaj Jain, Anastasia Molchanova, Jain, Pankaj +5
Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2004.12712

openalex publication_date 2020/04/27 · openalex created_date 2022/07/19 · openalex updated_date 2026/07/28

Abstract

We obtain a pointwise description of functions belonging to function spaces\nwith the lattice property. In particular, it is valid for Banach function\nspaces provided that the Hardy-Littlewood maximal operator is bounded. We also\nstudy weighted grand Sobolev spaces, defined on arbitrary open sets (of finite\nor infinite measure), and provide pointwise description of them.\n

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