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arXiv · 1210.3186

Sobolev and Hardy-Sobolev spaces on graphs

Emmanuel Russ·Maamoun Turkawi
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Abstract

Let $Γ$ be a graph. Under suitable geometric assumptions on $Γ$, we give several equivalent characterizations of Sobolev and Hardy-Sobolev spaces on $Γ$, in terms of maximal functionals, Hajł asz type functionals or atomic decompositions. As an application, we study the boundedness of Riesz transforms on Hardy spaces on $Γ$. This gives the discrete counterpart of the corresponding results on Riemannian manifolds.

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Emmanuel Russ, Maamoun Turkawi. 2012-10-11. Sobolev and Hardy-Sobolev spaces on graphs. https://arxiv.org/abs/1210.3186

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