TY - JOUR

T1 - Correction to

T2 - On the heterogeneous distortion inequality (Mathematische Annalen, (2022), 384, 3-4, (1275-1308), 10.1007/s00208-021-02315-2)

AU - Kangasniemi, Ilmari

AU - Onninen, Jani

N1 - Publisher Copyright:
© 2023, Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

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U2 - 10.1007/s00208-023-02728-1

DO - 10.1007/s00208-023-02728-1

M3 - Comment/Debate/Erratum

AN - SCOPUS:85173902263

SN - 0025-5831

JO - Mathematische Annalen

JF - Mathematische Annalen

ER -