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• W3098821553 abstract "We prove scaling invariant Gagliardo–Nirenberg type inequalities of the form begin{equation*} |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 }} textrm {d}x ; textrm {d}y right )^{gamma }, end{equation*} involving fractional Sobolev norms with $s>0$ and Coulomb type energies with $0<alpha <d$ and $qge 1$. We establish optimal ranges of parameters for the validity of such inequalities and discuss the existence of the optimizers. In the special case $p=frac {2d}{d-2s}$ our results include a new refinement of the fractional Sobolev inequality by a Coulomb term. We also prove that if the radial symmetry is taken into account, then the ranges of validity of the inequalities could be extended and such a radial improvement is possible if and only if $alpha >1$." @default.
• W3098821553 created "2020-11-23" @default.
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• W3098821553 date "2018-08-09" @default.
• W3098821553 modified "2023-10-07" @default.
• W3098821553 title "Sharp Gagliardo–Nirenberg inequalities in fractional Coulomb–Sobolev spaces" @default.
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• W3098821553 doi "https://doi.org/10.1090/tran/7426" @default.
• W3098821553 hasPublicationYear "2018" @default.
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