8 citations · 22 across the 8 of their papers we have counts for
11 papers
Functionals for Multilinear Fractional Embedding
William Beckner
A novel representation is developed as a measure for multilinear fractional embedding. Corresponding extensions are given for the Bourgain-Brezis-Mironescu theorem and Pitt's inequ…
Multilinear Embedding and Hardy's Inequality
William Beckner
Multilinear trace restriction inequalities are obtained for Hardy's inequality. More generally, detailed development is given for new multilinear forms for Young's convolution ineq…
Embedding estimates and fractional smoothness
William Beckner
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 geome…
Multilinear Embedding -- convolution estimates on smooth submanifolds
William Beckner
Multilinear embedding estimates for the fractional Laplacian are obtained in terms of functionals defined over a hyperbolic surface. Convolution estimates used in the proof enlarge…
Convolution estimates and the Gross-Pitaevskii hierarchy
William Beckner
Extensions to higher-dimensions are given for a convolution estimate used by Klainerman and Machedon in their study of uniqueness of solutions for the Gross-Pitaevskii hierarchy. S…
Multilinear embedding estimates for the fractional Laplacian
William Beckner
Three novel multilinear embedding estimates for the fractional Laplacian are obtained in terms of trace integrals restricted to the diagonal. The resulting sharp inequalities may b…