Embedding estimates and fractional smoothness

William Beckner

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arXiv · 1206.4215

Embedding estimates and fractional smoothness

William Beckner

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Abstract

A short intrinsic proof is given for the Bourgain-Brezis-Mironescu theorem with an extension for higher-order gradient forms. This argument illustrates the role of functional geometry and Fourier analysis for obtaining embedding estimates. New Hausdorff-Young inequalities are obtained for fractional embedding as an extension of the classical Aronszajn-Smith formula. These results include bilinear fractional embedding as suggested by the Landau collision operator in plasma dynamics.

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William Beckner. 2012-08-01. Embedding estimates and fractional smoothness. https://arxiv.org/abs/1206.4215

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