An L1-type estimate for Riesz potentials

Armin Schikorra, Daniel Spector, Jean Van Schaftingen

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)291-303
Number of pages13
JournalRevista Matematica Iberoamericana
Volume33
Issue number1
DOIs
Publication statusPublished - 2017
Externally publishedYes

Keywords

  • Fractional gradient
  • Riesz potentials
  • Riesz transforms
  • Sobolev inequalities

ASJC Scopus subject areas

  • Mathematics(all)

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