Sharp Gagliardo-Nirenberg inequalities in fractional Coulomb-Sobolev spaces

Jacopo Bellazzini, Marco Ghimenti, Carlo Mercuri +2

We prove scaling invariant Gagliardo-Nirenberg type inequalities of the form $$\|φ\|_{L^p(\mathbb{R}^d)}\le C\|φ\|_{\dot H^{s}(\mathbb{R}^d)}^β \left(\iint_{\mathbb{R}^d \times \ma…