An improvement to the John-Nirenberg inequality for functions in critical Sobolev spaces

Ángel D. Martínez, Daniel Spector*

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

摘要

It is known that functions in a Sobolev space with critical exponent embed into the space of functions of bounded mean oscillation, and therefore satisfy the John-Nirenberg inequality and a corresponding exponential integrability estimate. While these inequalities are optimal for general functions of bounded mean oscillation, the main result of this paper is an improvement for functions in a class of critical Sobolev spaces. Precisely, we prove the inequality Hβ ({x ∈ Ω: |Iαf(x)| > t}) ≤ Ce−ctq for all ||f||LN/α,q(Ω) ≤ 1 and any β ∈ (0, N], where Ω ⊂ RN, Hβ is the Hausdorff content, LN/α,q(Ω) is a Lorentz space with q ∈ (1, ∞], q' = q/(q − 1) is the Hölder conjugate to q, and Iαf denotes the Riesz potential of f of order α ∈ (0, N).

原文英語
頁(從 - 到)877-894
頁數18
期刊Advances in Nonlinear Analysis
10
發行號1
DOIs
出版狀態已發佈 - 2021 一月 1
對外發佈

ASJC Scopus subject areas

  • 分析

指紋

深入研究「An improvement to the John-Nirenberg inequality for functions in critical Sobolev spaces」主題。共同形成了獨特的指紋。

引用此