An application of the regularized Siegel-Weil formula on unitary groups to a theta lifting problem

Let U(2) and U(2; 1) be the pair of unitary groups over a global field F and pi an irreducible cuspidal representation of U(2) which satisfies a certain L-function condition. By using a regularized Siegel-Weil formula, we can show that the global theta lifting of pi in U(2; 1) is non-trivial if every local factor pi(v) of pi has a local theta lifting (Howe lifting) in U(2; 1)(F-v).