  We established a generalized version of the Christ-Kiselev's multi-linear
operator technique to deal with the spectral theory of Schr\"odinger operators.
As applications, several spectral results of perturbed periodic Schr\"odinger
operators are obtained, including WKB solutions, sharp transitions of
preservation of absolutely continuous spectra, criteria of absence of singular
spectra and sharp bounds of the Hausdorff dimension of singular spectra.
