Pitt’s inequality with sharp convolution estimates
Pitt’s inequality with sharp convolution estimates
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DOI：
10.1090/s0002-9939-07-09216-7
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发表时间：
2006-12
期刊：
影响因子：
--
通讯作者：
W. Beckner
中科院分区：
文献类型：
--
作者：
W. Beckner
Sharp L P extensions of Pitt's inequality expressed as a weighted Sobolev inequality are obtained using convolution estimates and Stein-Weiss potentials. Optimal constants are obtained for the full Stein-Weiss potential as a map from L P to itself which in turn yield semi-classical Rellich inequalities on R n . Additional results are obtained for Stein-Weiss potentials with gradient estimates and with mixed homogeneity. New proofs are given for the classical Pitt and Stein-Weiss estimates.
