New thoughts on fractional Sobolev spaces

Angha Agarwal; Pekka Koskela; Khanh Nguyen

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arXiv · 2610.35279

New thoughts on fractional Sobolev spaces

Angha Agarwal·Pekka Koskela·Khanh Nguyen

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Abstract

We introduce the concept of a fractional upper gradient and employ it to characterize the $p$-Muckenhoupt weighted $s$-fractional $p$-Sobolev spaces on $\mathbb R^d$ where $d\in\mathbb N$, $1<p<\infty$ and $0<s<1$.

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Angha Agarwal, Pekka Koskela, Khanh Nguyen. 2026-10-26. New thoughts on fractional Sobolev spaces. https://arxiv.org/abs/2610.35279

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