Weighted inequalities and Stein-Weiss potentials
By William Beckner. 2006
71 citations recorded by the source corpus.
Abstract Sharp extensions of Pitt's inequality and bounds for Stein-Weiss fractional integrals are obtained that incorporate gradient forms and vector-valued operators. Such results include Hardy-Rellich inequalities. 2000 Mathematics Subject Classification: 58J70, 42B10, 35A15.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/f2c421688038b09a4a0da76f87f0275329c7acee
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In Applied Mathematics
- Nguyen Huong Lam
- G. Lu
- Jie Liao
- Chunjin Lin
- Radjesvarane Alexandre
- William Beckner
- Caifeng Zhang
- Hanli Tang
Citations in the corpus
- Pitt's inequality and the fractional Laplacian: Sharp error estimates (2007, background): “The proofs given for the calculation of optimal constants for diagonal maps have some overall similarity, but the arguments given by the author ([6], [8], [12], [13]) emphasize the geometric symmetry corresponding to dilation invariance and characterize the operators in terms of convolution, as does”
- Some A priori estimates for the homogeneous Landau equation with soft potentials (2013, methodology): “We use Pitt’s inequality [4, 5, 6] to get that”
- Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications ✩ (2012, background): “We refer the reader to [11] for some nonexistence result of extremal functions for Stein–Weiss inequalities on the Heisenberg group by Beckner (see also [10,12] for Stein–Weiss inequalities in the Euclidean spaces).”