Measuring Triebel-Lizorkin fractional smoothness on domains in terms of first-order differences

@article{Prats2019MeasuringTF,
title={Measuring Triebel-Lizorkin fractional smoothness on domains in terms of first-order differences},
author={Mart'i Prats},
journal={J. Lond. Math. Soc.},
year={2019},
volume={100},
pages={692-716}
}
• Mart'i Prats
• Published 2019
• Mathematics, Computer Science
• J. Lond. Math. Soc.
In this note we give equivalent characterizations for a fractional Triebel-Lizorkin space $F^s_{p,q}(\Omega)$ in terms of first-order differences in a uniform domain $\Omega$. The characterization is valid for any positive, non-integer real smoothness $s\in \mathbb{R}_+\setminus \mathbb{N}$ and finite indices $p,q>1$ as long as the fractional part $\{s\}$ is greater than $d/p-d/q$.
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