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arXiv · 1612.00243

Sharp Gagliardo-Nirenberg inequalities in fractional Coulomb-Sobolev spaces

Jacopo Bellazzini·Marco Ghimenti·Carlo Mercuri·Vitaly Moroz·Jean Van Schaftingen
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Abstract

We prove scaling invariant Gagliardo-Nirenberg type inequalities of the form $$\|\varphi\|_{L^p(\mathbb{R}^d)}\le C\|\varphi\|_{\dot H^{s}(\mathbb{R}^d)}^{\beta} \left(\iint_{\mathbb{R}^d \times \mathbb{R}^d} \frac{|\varphi (x)|^q\,|\varphi (y)|^q}{|x - y|^{d-\alpha}} dx dy\right)^{\gamma},$$ involving fractional Sobolev norms with $s>0$ and Coulomb type energies with $0<\alpha 1$.

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BibTeXRIS

Jacopo Bellazzini, Marco Ghimenti, Carlo Mercuri, Vitaly Moroz, Jean Van Schaftingen. 2016-12-01. Sharp Gagliardo-Nirenberg inequalities in fractional Coulomb-Sobolev spaces. https://doi.org/10.1090/tran%2F7426

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