A unified approach to Carleson measures and \(A_ p\) weights. II (Q1102481)

We find for each p, \(1<p<\infty\), a necessary and sufficient condition on the pair (\(\mu\),\(\nu)\) (where \(\mu\) is a measure on \({\mathbb{R}}_+^{n+1}={\mathbb{R}}^ n\times [0,\infty)\), and \(\nu\) a weight on \({\mathbb{R}}^ n)\) for the Poisson integral to be a bounded operator from \(L^ p({\mathbb{R}}^ n,\nu (x)dx)\) into \(L^ p({\mathbb{R}}_+^{n+1},\mu).\) [For part I see ibid. (to appear).]