Sharp Higher Integrability Theory, Part I: The L^p-norm of the Beurling--Ahlfors transform

Abstract

We confirm a conjecture posed by T. Iwaniec in 1982: the L^p norm of the Beurling--Ahlfors transform is p−1 if p≥ 2, and (p−1)⁻¹ if 1<p≤ 2.

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BibTeX RIS

BibTeX

@misc{agazzi2026sharp,
  title = {{Sharp Higher Integrability Theory, Part I: The $L^p$-norm of the Beurling--Ahlfors transform}},
  author = {Andrea Agazzi and Kari Astala and Rodrigo Bañuelos and Giuseppe Bruno and Gabriele Cassese and Daniel Faraco and André Guerra and Mahdi Hormozi and Bernd Kirchheim and Aleksis Koski and Vjekoslav Kovač and Jan Kristensen and Federico Pasqualotto and István Prause and Eero Saksman and Vladimír Šverák and László Székelyhidi and Riccardo Tione and Alexander Volberg and Hang Yang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.28311},
  eprint = {2609.28311},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28311},
}

RIS

TY  - UNPB
TI  - Sharp Higher Integrability Theory, Part I: The L^p-norm of the Beurling--Ahlfors transform
AU  - Andrea Agazzi
AU  - Kari Astala
AU  - Rodrigo Bañuelos
AU  - Giuseppe Bruno
AU  - Gabriele Cassese
AU  - Daniel Faraco
AU  - André Guerra
AU  - Mahdi Hormozi
AU  - Bernd Kirchheim
AU  - Aleksis Koski
AU  - Vjekoslav Kovač
AU  - Jan Kristensen
AU  - Federico Pasqualotto
AU  - István Prause
AU  - Eero Saksman
AU  - Vladimír Šverák
AU  - László Székelyhidi
AU  - Riccardo Tione
AU  - Alexander Volberg
AU  - Hang Yang
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.28311
UR  - https://arxiv.org/abs/2609.28311
AB  - We confirm a conjecture posed by T. Iwaniec in 1982: the L^p norm of the Beurling--Ahlfors transform is p−1 if p≥ 2, and (p−1)^−1 if 1<p≤ 2.
ER  -

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