The Euclidean Onofri Inequality in Higher Dimensions
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2013Metadata
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Pino Manresa, Manuel del
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The Euclidean Onofri Inequality in Higher Dimensions
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The classical Onofri inequality in the two-dimensional sphere assumes a natural form
in the plane when transformed via stereographic projection. We establish an optimal
version of a generalization of this inequality in the d-dimensional Euclidean space for
any d≥ 2, by considering the endpoint of a family of optimal Gagliardo–Nirenberg interpolation
inequalities. Unlike the two-dimensional case, this extension involves a rather
unexpected Sobolev–Orlicz norm, as well as a probability measure no longer related to
stereographic projection.
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International Mathematics Research Notices, Vol. 2013, No. 15, pp. 3600–3611
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