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# Lower bounds for Coulomb energy for functions in homogeneous fractional sobolev spaces

Ponente: Marco Ghimenti
We prove $$L^p$$ lower bounds for Coulomb energy for radially
symmetric functions in $$\dot{H}^s(\mathbb{R}^3)$$ with $$1/2 <s< 3/2$$. By this bound we can improve sobolev embedding for radial
functions in $$\dot{H}^s(\mathbb{R}^3)$$ with bounded Coulomb
energy.  This result is sharp for $$1/2<s<1$$.