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PARIS - Serena Williams won her fourth-round match and won over French Open fans Sunday.
Jeered earlier in the tournament, Williams drew only cheers after beating Shinobu Asagoe 6-3, 6-1.
Williams was joined in Tuesday's quarterfinals by older sister Venus, who beat Fabiola Zuluaga 6-1, 7-6 (6-3). The sisters could meet in the semifinals.
No.7 seed Jennifer Capriati overcame a thigh strain to beat No.17 Francesca Schiavone 7-5, 6-1 and plays Serena Williams.
Second-seeded Williams committed six unforced errors in the first game and fell behind 2-0 but dominated the rest of the way. She smacked 24 winners to Asagoe's three.
"I'm definitely improving match after match," Williams said. "I'm just getting better as each match goes on. It's going to be a good second week."
The 2002 champion closed the victory when she put away a swinging volley from the baseline. She curtsied and smiled as the crowd applauded.
Scattered whistles and boos were directed at Williams late in her second-round victory. The jeers were less hostile than last year, when she lost a tumultuous semifinal to Justine Henin-Hardenne.
Venus Williams raced to a 5-0 lead against the No.23 Zuluaga but struggled down the stretch. Plagued by injuries that included an abdominal strain last year, Williams appeared to clutch her stomach and wince at least twice but still hit 28 winners.
She was broken serving for the second set, then rallied from a 2-0 deficit in the tiebreaker.
"While I would have liked to have had an easier match, I think it's important for me to be tested early on," said Williams, seeded fourth.
Williams' quarterfinal opponent is No.6 Anastasia Myskina, who overcame a match point to beat Svetlana Kuznetsova 1-6, 6-4, 8-6.
Capriati required treatment for a strained right thigh against Schiavone but lost 11 points - three on double faults - in the final 10 games.
"I should always get injured like that," Capriati joked. "I don't think it's really severe. I think if it was really severe, I wouldn't have been able to keep moving like I did."
Unable to overcome an injury was Lindsay Davenport, who lost again in the only Grand Slam event she has not won. Hampered by a sore right knee, the No.5 seed was beaten by Elena Dementieva 6-1, 6-3.
Davenport said she hurt the knee in the second round Wednesday and aggravated it in the second set against Dementieva.
"From then on it was really sore," Davenport said. "I was just trying to go for shots, kind of knowing that it was probably not going to happen."
Davenport missed three Grand Slam events after arthroscopic knee surgery in 2002. She plans to have this injury evaluated when she returns to California.
"I'll be extremely bummed if it means more time away," she said.
Joining Myskina and Dementieva in the quarterfinals was a third Russian, Maria Sharapova, who beat Marlene Weingartner 6-3, 6-1 to reach the final eight at a Grand Slam event for the first time.
"It's an amazing accomplishment," the 17-year-old said. "I'm really looking forward to playing some great tennis in the next round, just like I've been doing this whole week."
No.3 Amelie Mauresmo beat No.21 Magdalena Maleeva 6-2, 6-1. Mauresmo faces Dementieva.
Zheng Jie became the first Chinese woman to play a fourth-round match at a Grand Slam event but lost to No.14 Paola Suarez 6-4, 7-5.
On the men's side, No.9 Tim Henman earned his first quarterfinal berth in a major other than Wimbledon by rallying past wild-card Michael Llodra 6-7 (2-6), 4-6, 6-4, 6-3, 9-7.
Henman overcame a match point serving at 4-5 in the final set. His opponent is No.22 Juan Ignacio Chela, who became a first-time Grand Slam quarterfinalist by beating Olivier Mutis 4-6, 6-2, 7-6 (7-5), 6-2. Mutis upset Andy Roddick in the second round.
No.3 Guillermo Coria advanced when Nicolas Escude retired with tendinitis in his right shoulder after losing the first set 6-0. Coria has dropped 21 games in four rounds.
Coria's quarterfinal opponent is No.5 Carlos Moya, the 1998 champion, who beat fellow Spaniard Tommy Robredo 7-6 (8-6), 6-4, 6-2.
Xavier Malisse won the last third-round match, beating 2002 champion Albert Costa 6-4, 2-6, 4-6, 7-6 (6-4), 8-6. Malisse overcame two match points before play was suspended in the fourth set Saturday because of darkness.