An optimal Sobolev embedding for L1

Daniel Spector

doi:10.1016/j.jfa.2020.108559

An optimal Sobolev embedding for L¹

Daniel Spector^*

^*Corresponding author for this work

Department of Mathematics

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

21 Citations (Scopus)

Abstract

In this paper we establish an optimal Lorentz space estimate for the Riesz potential acting on curl-free vectors: There is a constant C=C(α,d)>0 such that ‖I_αF‖_{L^d/(d−α),1(R^d;R^d)}≤C‖F‖_L¹(R^d;R^d) for all fields F∈L¹(R^d;R^d) such that curlF=0 in the sense of distributions. This is the best possible estimate on this scale of spaces and completes the picture in the regime p=1 of the well-established results for p>1.

Original language	English
Article number	108559
Journal	Journal of Functional Analysis
Volume	279
Issue number	3
DOIs	https://doi.org/10.1016/j.jfa.2020.108559
Publication status	Published - 2020 Aug 15

Keywords

L-type estimates
Riesz potentials
Sobolev embeddings

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2020.108559

Cite this

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KW - Sobolev embeddings

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