標題: An optimal Sobolev embedding for L-1
作者: Spector, Daniel
應用數學系
Department of Applied Mathematics
關鍵字: Sobolev embeddings;L-1-type estimates;Riesz potentials
公開日期: 15-Aug-2020
摘要: In this paper we establish an optimal Lorentz space estimate for the Riesz potential acting on curl-free vectors: There is a constant C = C(alpha, d) > 0 such that parallel to L alpha F parallel to(Ld/(d-alpha),1(Rd;Rd)) <= C parallel to F parallel to(L1(Rd;Rd)) for all fields F is an element of L-1 (R-d;R-d) such that curl F = 0 in the sense of distributions. This is the best possible estimate on this scale of spaces and completes the picture in the regime p = 1 of the well-established results for p > 1. (C) 2020 The Author. Published by Elsevier Inc.
URI: http://dx.doi.org/10.1016/j.jfa.2020.108559
http://hdl.handle.net/11536/154328
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2020.108559
期刊: JOURNAL OF FUNCTIONAL ANALYSIS
Volume: 279
Issue: 3
起始頁: 0
結束頁: 0
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