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math.AP2007★ 1 cited
Pitt's inequality with sharp convolution estimates
William Beckner
Sharp extensions of Pitt's inequality expressed as a weighted Sobolev inequality are obtained using convolution estimates and Stein-Weiss potentials. More generally, optimal…
math.AP1999
On the Grushin operator and hyperbolic symmetry
William Beckner
Complexity of geometric symmetry for differential operators with mixed homogeniety is examined here. Sharp Sobolev estimates are calculated for the Grushin operator in low dimensio…