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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