2012/06/19 by Beckner, William
#58 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1206.4215
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.