An L 1 -type estimate for Riesz potentials

Armin Schikorra; Eli Spector; Jean Van Schaftingen

doi:10.4171/rmi/937

An L ¹ -type estimate for Riesz potentials

Armin Schikorra
, Eli Spector
, Jean Van Schaftingen

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研究成果: Article › 同行評審

42 引文斯高帕斯（Scopus）

摘要

In this paper we establish new L¹-type estimates for the classical Riesz potentials of order α ∈ (0,N): ||Iαu|| L^N/(N-α)(ℝN) le; C||Ru|| L¹(ℝ^N; ℝ^N). This sharpens the result of Stein and Weiss on the mapping properties of Riesz potentials on the real Hardy space H¹(ℝ^N) and provides a new family of L¹-Sobolev inequalities for the Riesz fractional gradient.

原文	English
頁（從 - 到）	291-303
頁數	13
期刊	Revista Matematica Iberoamericana
卷	33
發行號	1
DOIs	https://doi.org/10.4171/rmi/937
出版狀態	Published - 2017

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title = "An L 1 -type estimate for Riesz potentials",

abstract = "In this paper we establish new L1-type estimates for the classical Riesz potentials of order α ∈ (0,N): ||Iαu|| LN/(N-α)(ℝN) le; C||Ru|| L1(ℝN; ℝN). This sharpens the result of Stein and Weiss on the mapping properties of Riesz potentials on the real Hardy space H1(ℝN) and provides a new family of L1-Sobolev inequalities for the Riesz fractional gradient.",

keywords = "Fractional gradient, Riesz potentials, Riesz transforms, Sobolev inequalities",

author = "Armin Schikorra and Eli Spector and \{Van Schaftingen\}, Jean",

note = "Publisher Copyright: {\textcopyright} European Mathematical Society.",

year = "2017",

doi = "10.4171/rmi/937",

language = "English",

volume = "33",

pages = "291--303",

journal = "Revista Matematica Iberoamericana",

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T1 - An L 1 -type estimate for Riesz potentials

AU - Schikorra, Armin

AU - Spector, Eli

AU - Van Schaftingen, Jean

N1 - Publisher Copyright: © European Mathematical Society.

PY - 2017

Y1 - 2017

N2 - In this paper we establish new L1-type estimates for the classical Riesz potentials of order α ∈ (0,N): ||Iαu|| LN/(N-α)(ℝN) le; C||Ru|| L1(ℝN; ℝN). This sharpens the result of Stein and Weiss on the mapping properties of Riesz potentials on the real Hardy space H1(ℝN) and provides a new family of L1-Sobolev inequalities for the Riesz fractional gradient.

AB - In this paper we establish new L1-type estimates for the classical Riesz potentials of order α ∈ (0,N): ||Iαu|| LN/(N-α)(ℝN) le; C||Ru|| L1(ℝN; ℝN). This sharpens the result of Stein and Weiss on the mapping properties of Riesz potentials on the real Hardy space H1(ℝN) and provides a new family of L1-Sobolev inequalities for the Riesz fractional gradient.

KW - Fractional gradient

KW - Riesz potentials

KW - Riesz transforms

KW - Sobolev inequalities

UR - https://www.scopus.com/pages/publications/85016400632

U2 - 10.4171/rmi/937

DO - 10.4171/rmi/937

M3 - Article

AN - SCOPUS:85016400632

SN - 0213-2230

VL - 33

SP - 291

EP - 303

JO - Revista Matematica Iberoamericana

JF - Revista Matematica Iberoamericana

IS - 1

ER -

An L 1 -type estimate for Riesz potentials

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An L ¹ -type estimate for Riesz potentials