So far, so good for Naomi Osaka and her new coach at the US Open

NEW YORK (AP) — Naomi Osaka is back in the third round of the U.S. Open for the first time since 2021, the year after she won her second championship at Flushing Meadows. She's playing rather well at the moment, too, under the guidance of a new coach. Just don't expect Osaka to weigh in on whether she feels as if she is ready to make another deep run at the place. "Honestly, I don't really know. I don't make it my business to know anymore. I kind of just leave it up in the air," the 23rd-seeded Osaka said after eliminating Hailey Baptiste 6-3, 6-1 in the second round in just 70 minutes Thursday. "For me, I realize that I've done everything that I could. I've trained really hard. I practiced really hard. If it happens, it happens." Osaka's four Grand Slam trophies all arrived on hard courts: two at the U.S. Open, two at the Australian Open. Since her 2020 title in New York, her trips there have gone this way: losses in the third round in 2021, first round in 2022, second round last year. The surface tends to favor the big serves and powerful, first-strike tennis Osaka is best known for, and something she displayed against Baptiste, of course, although she also demonstrated a willingness to vary speeds and spins. The other talent Osaka is using to great effect so far this week is returning that gets an opponent on the defensive. Osaka already has won 11 of the 18 return games she's played so far, including during a 6-3, 6-4 win over Greet Minnen in the first round. After her third-round exit at Wimbledon last month, Osaka split from coach Patrick Mouratoglou and began working with Tomasz Wiktorowski, who used to be part of Iga Swiatek's team. One key, Osaka said: Wiktorowski has encouraged her to focus more on the placement of her shots "and not necessarily going for winners most of the time." They appear to be making quick progress — and Osaka said her impression of him changed quickly. "Honestly, I didn't know him, I thought he was very scary, because he's very tall and he didn't smile," she said. "Now that we're working together, I see that he smiles often. He has a very friendly smile, and it's very nice. That's my little fun fact about Tomasz." Venus Williams gets a US Open women's doubles victory Venus Williams earned her first win in a U.S. Open women's doubles match since 2014 — and this time, her partner wasn't younger sister Serena but Leylah Fernandez. The 45-year-old Williams, who recently returned to the tour after a 16-month absence, and Fernandez eliminated the sixth-seeded pair of Lyudmyla Kichenok and Ellen Perez 7-6 (4), 6-3. What else happened at the US Open on Thursday? Wimbledon champions Swiatek and Jannik Sinner both won — his victory was much more straightforward than hers. Swiatek had some trouble before getting past Suzan Lamens, a Dutch player ranked 66th who'd never appeared at a Grand Slam tournament until this year, by a 6-1, 4-6, 6-4 score. Sinner was just fine in a 6-3, 6-2, 6-2 win against Alexei Popyrin, who beat Novak Djokovic at the U.S. Open a year ago. Who is on Friday's schedule at the US Open? Carlos Alcaraz, the 2022 men's champion, and Jessica Pegula, the 2024 women's runner-up, play their third-round matches in Arthur Ashe Stadium during the day session. Djokovic, owner of 24 Grand Slam titles, meets Cam Norrie in Ashe at night, followed by American Taylor Townsend — who got into a back-and-forth with her opponent, Jelena Ostapenko, after their second-round match — against No. 5 seed Mirra Andreeva, an 18-year-old from Russia.