• 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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