Osaka, who grew up in the US and speaks little Japanese, melted hearts when she fought back tears after her emotional US Open win over her idol Williams as booing echoed around the stadium.
Bajin responded to Osaka and thanked her "for letting me be a part of this".
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He's really competitive and that's why he's played this many games. "He has been, and remains, a fantastic captain". We have great memories of this stadium. "His adaptation has been very fast", Solari said.
"I will no longer be working together with Sascha", tweeted the USA -based Japanese 21-year-old.
"Thank you Naomi I wish you nothing but the best as well". I wish you nothing but the best as well.
An ex-ATP tour player, Bajin won 13 Grand Slams while in the Serena camp, including all four major tournaments and a hat-trick of Wimbledon and US Open titles in a partnership that lasted from 2008 to 2015.
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Bajin took up the coach's job with Osaka in 2017 and experienced immediate success.
By winning a second grand slam and becoming world No 1, she firmly established herself as at the forefront of the next generation of women players.
The 21-year-old added the Australian Open to her growing list of honours in January and consequently topped the world rankings for the first time in her career.
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Negotiations in Washington last month ended without a deal and with the top US negotiator declaring work was needed. It has also imposed a 10 percent tariff on another $200 billion of made-in-China goods.