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• W1966266564 abstract "A reduction theorem is established, showing that any Sobolev inequality, involving arbitrary rearrangement-invariant norms with respect to the Gauss measure in R n , is equivalent to a one-dimensional inequality, for a suitable Hardy-type operator, involving the same norms with respect to the standard Lebesgue measure on the unit interval. This result is exploited to provide a general characterization of optimal range and domain norms in Gaussian Sobolev inequalities. Applications to special instances yield optimal Gaussian Sobolev inequalities in Orlicz and Lorentz(–Zygmund) spaces, point out new phenomena, such as the existence of self-optimal spaces, and provide further insight into classical results." @default.
• W1966266564 created "2016-06-24" @default.
• W1966266564 creator A5049276347 @default.
• W1966266564 creator A5075871069 @default.
• W1966266564 date "2009-06-01" @default.
• W1966266564 modified "2023-10-04" @default.
• W1966266564 title "Optimal Gaussian Sobolev embeddings" @default.
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• W1966266564 doi "https://doi.org/10.1016/j.jfa.2009.03.001" @default.
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