  We provide a uniform estimate for the $L^1$-norm (over any interval of
bounded length) of the logarithmic derivatives of global normalizing factors
associated to intertwining operators for the following reductive groups over
number fields: inner forms of $GL(n)$; quasi-split classical groups and their
similitude groups; the exceptional group $G_2$. This estimate is a key
ingredient in the analysis of the spectral side of Arthur's trace formula. In
particular, it is applicable to the limit multiplicity problem studied by the
authors in earlier papers.
