Embedding Estimates and Fractional Smoothness
2014
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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