Some remarks on L1 embeddings in the subelliptic setting

Steven G. Krantz, Marco M. Peloso, Daniel Spector*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we establish an optimal Lorentz estimate for the Riesz potential in the L1 regime in the setting of a stratified group G: Let Q≥2 be the homogeneous dimension of G and Iα denote the Riesz potential of order α on G. Then, for every α∈(0,Q), there exists a constant C=C(α,Q)>0 such that ‖Iαf‖LQ∕(Q−α),1(G)≤C‖XI1f‖L1(G)for all f∈Cc(G) such that XI1f∈L1(G), where X denotes the horizontal gradient.

Original languageEnglish
Article number112149
JournalNonlinear Analysis, Theory, Methods and Applications
Volume202
DOIs
Publication statusPublished - 2021 Jan
Externally publishedYes

Keywords

  • L regime
  • Lorentz spaces
  • Sobolev embeddings
  • Stratified group
  • Subelliptic estimates

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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