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arXiv · 2405.07329

New approach to affine Moser-Trudinger inequalities via Besov polar projection bodies

Oscar Dominguez·Yinqin Li·Sergey Tikhonov·Dachun Yang·Wen Yuan
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Abstract

We extend the affine inequalities on $\mathbb{R}^n$ for Sobolev functions in $W^{s,p}$ with $1 \leq p < n/s$ obtained recently by Haddad-Ludwig [16, 17] to the remaining range $p \geq n/s$. For each value of $s$, our results are stronger than affine Moser-Trudinger and Morrey inequalities. As a byproduct, we establish the analog of the classical $L^p$ Bourgain-Brezis-Mironescu inequalities related to the Moser-Trudinger case $p=n$. Our main tool is the affine invariant provided by Besov polar projection bodies.

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Oscar Dominguez, Yinqin Li, Sergey Tikhonov, Dachun Yang, Wen Yuan. 2024-05-12. New approach to affine Moser-Trudinger inequalities via Besov polar projection bodies. https://arxiv.org/abs/2405.07329

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