• Corpus ID: 251594575

Distributional Fractional Gradients and a Bourgain-Brezis-type Estimate

@inproceedings{Wettstein2022DistributionalFG,
  title={Distributional Fractional Gradients and a Bourgain-Brezis-type Estimate},
  author={J Wettstein},
  year={2022}
}
In this paper, we extend the definition of fractional gradients found in Mazowiecka-Schikorra [6] to tempered distributions on R n , introduce associated regularisation procedures and establish some first regularity results for distributional fractional gradients in L 1 od . The key feature is the introduction of a suitable space of off-diagonal Schwarz functions S od ( R 2 n ), allowing for a dual definition of the fractional gradient on an appropriate space of distributions S ′ od ( R 2 n ) by… 

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