Correction to: On the heterogeneous distortion inequality (Mathematische Annalen, (2022), 384, 3-4, (1275-1308), 10.1007/s00208-021-02315-2)

Ilmari Kangasniemi, Jani Onninen

Research output: Contribution to journalComment/Debate/Erratumpeer-review

Abstract

We correct an error in [I. Kangasniemi, and J. Onninen, On the heterogeneous distortion inequality. Math. Ann. 384 (2022), no. 3-4, 1275–1308.]When investigating the potential alternate applications of the methods in our paper On the heterogeneous distortion inequality [3], we discovered that the presented proof of the main result, Theorem 1.3, has a critical flaw. This error occurs late in the paper, in the relatively technical proof of the lower integrability result shown in Lemma 7.2, and invalidates this lemma in its stated form. The only results in the paper affected by this error are Lemma 7.2 and Theorem 1.3. We have been unable to reprove the original statement of Lemma 7.2. However, in this corrigendum, we present a fix that recovers the main result, Theorem 1.3, in its entirety. The fix is non-trivial, and took us numerous failed attempts to find. The error in the proof of Lemma 7.2 lies in the use of the Hardy-Littlewood maximal inequality. In particular, we apply it on a subset of (Formula presented.). While there are maximal inequalities on more general domains, this requires that the definition of the maximal function is restricted to the domain; in our case, the definition of the maximal function extends past the domain, invalidating the inequality.

Original languageEnglish (US)
JournalMathematische Annalen
DOIs
StateAccepted/In press - 2023

ASJC Scopus subject areas

  • General Mathematics

Fingerprint

Dive into the research topics of 'Correction to: On the heterogeneous distortion inequality (Mathematische Annalen, (2022), 384, 3-4, (1275-1308), 10.1007/s00208-021-02315-2)'. Together they form a unique fingerprint.

Cite this