A Trace Inequality for Solenoidal Charges

Bogdan Raiţă, Daniel Spector*, Dmitriy Stolyarov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that for α ∈ (d − 1,d), one has the trace inequality∫ℝd|IαF|dν≤C|F|(ℝd)∥ν∥Md−α(ℝd) for all solenoidal vector measures F, i.e., F∈ Mb(ℝd; ℝd) and divF = 0. Here Iα denotes the Riesz potential of order α and ℳdα(ℝd) the Morrey space of (d − α)-dimensional measures on ℝd.

Original languageEnglish
JournalPotential Analysis
DOIs
Publication statusAccepted/In press - 2022

Keywords

  • Hausdorff content
  • L1 estimates
  • Riesz potential
  • Trace inequality

ASJC Scopus subject areas

  • Analysis

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