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Sharp Sobolev inequalities in Lorentz spaces for a mean oscillation |
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| Authors: | Norisuke Ioku |
| Institution: | Graduate School of Science and Engineering, Ehime University, Matsuyama, Ehime 790-8577, Japan |
| Abstract: | We exhibit the optimal constant for Sobolev inequalities in Lorentz spaces for a mean oscillation, and its relation with a boundedness of the Hardy–Littlewood maximal operator in Sobolev spaces. Some applications to a scale invariant form of Hardy?s inequality in a limiting case are also considered. |
| Keywords: | Sobolev inequalities in Lorentz spaces Optimal constant Critical Hardy inequalities Scale invariance property |
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