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A noninequality for the fractional gradient
https://oist.repo.nii.ac.jp/records/1561
https://oist.repo.nii.ac.jp/records/15614bc8dce4-41bd-4b88-8349-0cfbc995d966
Item type | 学術雑誌論文 / Journal Article(1) | |||||
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公開日 | 2020-06-22 | |||||
タイトル | ||||||
言語 | en | |||||
タイトル | A noninequality for the fractional gradient | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
資源タイプ | journal article | |||||
アクセス権 | ||||||
アクセス権 | metadata only access | |||||
アクセス権URI | http://purl.org/coar/access_right/c_14cb | |||||
著者(英) |
Spector, Daniel
× Spector, Daniel |
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書誌情報 |
en : Portugaliae Mathematica 巻 76, 号 2, p. 153-168, 発行日 2020-02-13 |
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抄録 | ||||||
内容記述タイプ | Other | |||||
内容記述 | In this paper we give a streamlined proof of an inequality recently obtained by the author: For every α∈(0,1) there exists a constant C=C(α,d)>0 such that [Formula: see text] for all u∈Lq(Rd) for some 1≤q<d/(1−α) such that Dαu:=∇I1−αu∈L1(Rd;Rd). We also give a counterexample which shows that in contrast to the case α=1, the fractional gradient does not admit an L1 trace inequality, i.e. [Formula: see text] cannot control the integral of u with respect to the Hausdorff content [Formula: see text]. The main substance of this counterexample is a result of interest in its own right, that even a weak-type estimate for the Riesz transforms fails on the space [Formula: see text], β∈[1,d). It is an open question whether this failure of a weak-type estimate for the Riesz transforms extends to β∈(0,1). |
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出版者 | ||||||
出版者 | European Mathematical Society | |||||
ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 0032-5155 | |||||
ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 1662-2758 | |||||
DOI | ||||||
識別子タイプ | DOI | |||||
関連識別子 | info:doi/10.4171/PM/2031 | |||||
権利 | ||||||
権利情報 | © 2020 EMS Publishing House. | |||||
関連サイト | ||||||
識別子タイプ | URI | |||||
関連識別子 | https://www.ems-ph.org/journals/show_abstract.php?issn=0032-5155&vol=76&iss=2&rank=4 | |||||
関連サイト | ||||||
識別子タイプ | URI | |||||
関連識別子 | https://arxiv.org/abs/1906.05541 | |||||
関連名称 | arXiv.org |