On the analytic properties of intertwining operators I: Global normalizing factors

We provide a uniform estimate for the L¹-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 G₂This 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.