Stabilisation de la formule des traces tordue IX : propri\'et\'es des int\'egrales orbitales pond\'er\'ees $\omega$ equivariantessurlecorpsr\'eel

In the preceeding article, we have generalized to the twisted case the proposition 3.1 of the third Arthur’s article on the stabilization of the trace formula. The base-field was p-adic. Here, we prove the same result over the real base-field. We prove also auxiliary results on the differential equations and the jump’s conditions satisfied by the weighted orbital integrals.