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- W4310888925 abstract "Let $mathcal{W}$ be a closed dilation and translation invariant subspace of the space of $mathbb{R}^ell$-valued Schwartz distributions in $d$ variables. We show that if the space $mathcal{W}$ does not contain distributions of the type $aotimes delta_0$, $delta_0$ being the Dirac delta, then the inequality $|mathbb{I}_alpha [f]|_{L_{p,1}}lesssim |f|_{L_1}$, $frac{p-1}{p} = frac{alpha}{d}$, holds true for functions $finmathcal{W}cap L_1$ with a uniform constant; here $mathbb{I}_alpha$ is the Riesz potential of order $alpha$ and $L_{p,1}$ is the Lorentz space. This result implies as a particular case the inequality $|nabla^{m-1} f|_{L_{frac{d}{d-1},1}} lesssim |A f|_{L_1}$, where $A$ is a canceling elliptic differential operator of order $m$." @default.
- W4310888925 created "2022-12-20" @default.
- W4310888925 creator A5087044944 @default.
- W4310888925 date "2020-10-11" @default.
- W4310888925 modified "2023-10-12" @default.
- W4310888925 title "Hardy--Littlewood--Sobolev inequality for $p=1$" @default.
- W4310888925 doi "https://doi.org/10.48550/arxiv.2010.05297" @default.
- W4310888925 hasPublicationYear "2020" @default.
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