The LIGO-Virgo Collaboration (LVC) detected, on 2017 August 17, an exceptional gravitational-wave (GW) event temporally consistent within $sim,1.7 , rm s$ with the GRB 1708117A observed by Fermi-GBM and INTEGRAL. The event turns out to be compatible with a neutron star-neutron star (NS-NS) coalescence that subsequently produced a radio/optical/X-ray transient detected at later times. We report the main results of the observations by the AGILE satellite of the GW170817 localization region (LR) and its electromagnetic (e.m.) counterpart. At the LVC detection time $T_0$, the GW170817 LR was occulted by the Earth. The AGILE instrument collected useful data before and after the GW-GRB event because in its spinning observation mode it can scan a given source many times per hour. The earliest exposure of the GW170817 LR by the gamma-ray imaging detector (GRID) started about 935 s after $T_0$. No significant X-ray or gamma-ray emission was detected from the LR that was repeatedly exposed over timescales of minutes, hours, and days before and after GW170817, also considering Mini-calorimeter and Super-AGILE data. Our measurements are among the earliest ones obtained by space satellites on GW170817 and provide useful constraints on the precursor and delayed emission properties of the NS-NS coalescence event. We can exclude with high confidence the existence of an X-ray/gamma-ray emitting magnetar-like object with a large magnetic field of $10^{15} , rm G$. Our data are particularly significant during the early stage of evolution of the e.m. remnant.
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