An L1-type estimate for Riesz potentials

被引：35

作者：

Schikorra, Armin ^{[1
]}

Spector, Daniel ^{[2
]}

Van Schaftingen, Jean ^{[3
]}

机构：

[1] Albert Ludwigs Univ, Abt Reine Math, Math Inst, Eckerstr 1, D-79104 Freiburg, Germany

[2] Natl Chiao Tung Univ, Dept Appl Math, 1001 Ta Hsueh Rd, Hsinchu, Taiwan

[3] Catholic Univ Louvain, Inst Rech Math & Phys, Chemin Cyclotron 2,Bte L7-01-01, B-1348 Louvain La Neuve, Belgium

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2017年 / 33卷 / 01期

关键词：

Riesz potentials; Riesz transforms; Sobolev inequalities; fractional gradient; EQUATION; SPACES;

D O I：

10.4171/RMI/937

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we establish new L-1-type estimates for the classical Riesz potentials of order alpha is an element of (0, N): parallel to I alpha u parallel to N-L/(N-alpha)(R-N) <= C parallel to Ru parallel to (L1(RN; RN)). This sharpens the result of Stein and Weiss on the mapping properties of Riesz potentials on the real Hardy space H-1 (R-N) and provides a new family of L-1-Sobolev inequalities for the Riesz fractional gradient.

引用

页码：291 / 303

页数：13

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