US Open statement on women's final:
On the fifth point in the second game of the second set between Naomi Osaka and Serena Williams, the chair umpire witnessed coaching taking place from Williams' coach. Even though her coach has admitted to coaching, Williams has made it clear that she did not receive any coaching. Nevertheless, in accordance with the rules, Williams was assessed a Code Violation, resulting in a warning.
At the completion of the fifth game of the second set, Williams was assessed a second code violation for racquet abuse, which required a point penalty.
At the changeover, at 4-3, Williams was assessed a third code violation for verbal abuse in the judgment of the umpire, which then required a game penalty.
The chair umpire's decision was final and not reviewable by the Tournament Referee or the Grand Slam Supervisor, who were called to the court at that time.