An L1-type estimate for Riesz potentials

Armin Schikorra; Daniel Spector; Jean Van Schaftingen

doi:10.4171/rmi/937

An L¹-type estimate for Riesz potentials

Armin Schikorra
, Daniel Spector
, Jean Van Schaftingen

Research output: Contribution to journal › Article › peer-review

42 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	291-303
Number of pages	13
Journal	Revista Matematica Iberoamericana
Volume	33
Issue number	1
DOIs	https://doi.org/10.4171/rmi/937
Publication status	Published - 2017
Externally published	Yes

Keywords

Fractional gradient
Riesz potentials
Riesz transforms
Sobolev inequalities

ASJC Scopus subject areas

General Mathematics

Access to Document

10.4171/rmi/937

Cite this

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title = "An L1-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 Daniel Spector and \{Van Schaftingen\}, Jean",

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journal = "Revista Matematica Iberoamericana",

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T1 - An L1-type estimate for Riesz potentials

AU - Schikorra, Armin

AU - Spector, Daniel

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

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JO - Revista Matematica Iberoamericana

JF - Revista Matematica Iberoamericana

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