Sharp Constants in Some Multiplicative Sobolev Inequalities

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0995-023.pdf (192.17 KB)
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Bobkov, S. G.
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http://hdl.handle.net/1853/31301
Abstract
The optimal constants in the multiplicative Sobolev inequalities where the gradient is estimated in the L_1-norm and the function in two different Lebesgue norms are found. With the optimal constants, these inequalities turn out to still be equivalent to the isoperimetric property of the balls in the Euclidean space. In the course of the proof, relations between Lorentz and Lebesgue spaces are studied (and also applied to some different measures, e.g., Riesz potentials).
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Bobkov: Research supported in part by the ISF grant NZX000 and NZX300. Houdré: Research supported in part by an NSF Postdoctoral Fellowship.
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1995-09-16
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