The Associated Press

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 a short time later by older sister Venus, who beat Fabiola Zuluaga 6-1, 7-6 (3). The sisters could meet in the semifinals.

No. 7-seeded Jennifer Capriati overcame a thigh strain to beat No. 17 Francesca Schiavone 7-5, 6-1 and will play Serena Williams next.

Second-seeded Serena 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 three for Asagoe.

"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. I'm real excited by it."

The 2002 champion closed the victory when she put away a swinging volley from the baseline - a shot most players wouldn't even attempt. She curtsied and smiled as the center court crowd applauded.

Scattered whistles and boos were directed at Williams late in her second-round victory. The jeers were less hostile than last year at Roland Garros, when she lost a tumultuous semifinal to Justine Henin-Hardenne.

Venus Williams raced to a 5-0 lead against the No. 23-seeded Zuluaga but struggled down the stretch. Williams, who has been plagued by injuries that included an abdominal strain last year, appeared to clutch her stomach and wince at least twice but was healthy enough to 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 Venus Williams, who's seeded fourth.

Serena Williams praised her sister's play of late. "She's been dominating me in practice, so I definitely have to pick up my game in the next match or two," Serena said.

Venus' opponent in the quarterfinals will be No. 6 Anastasia Myskina, who overcame a match point to beat Russian compatriot Svetlana Kuznetsova 1-6, 6-4, 8-6.

Capriati required treatment for a strained right thigh against Schiavone but lost only 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 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 never won. Erratic and hampered by a sore knee, the No. 5-seeded Davenport was beaten by Elena Dementieva 6-1, 6-3.

Davenport said she hurt her right knee in the second round Wednesday, then aggravated the injury 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 undergoing arthroscopic surgery on the knee in 2002. She plans to have the latest injury evaluated when she returns home to California.

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.

On the men's side, No. 9 Tim Henman earned his first quarterfinal berth in a major event other than Wimbledon by rallying past French wild-card Michael Llodra 6-7 (2), 4-6, 6-4, 6-3, 9-7.

Henman overcame a match point serving at 4-5 in the final set. His opponent Tuesday will be No. 22 Juan Ignacio Chela, who became a first-time Grand Slam quarterfinalist by beating Olivier Mutis 4-6, 6-2, 7-6 (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's quarterfinal opponent will be No. 5 Carlos Moya, the 1998 champion, who beat fellow Spaniard Tommy Robredo 7-6 (8), 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 (4), 8-6.

French Open glance

Top Men's Seeded Winners: No. 3 Guillermo Coria, No. 5 Carlos Moya, No. 9 Tim Henman. Women's Seeded Winners: No. 2 Serena Williams, No. 3 Amelie Mauresmo, No. 4 Venus Williams, No. 6 Anastasia Myskina, No. 7 Jennifer Capriati, No. 9 Elena Dementieva, No. 14 Paola Suarez, No. 18 Maria Sharapova.

Women's Seeded Losers: No. 5 Lindsay Davenport, No. 11 Svetlana Kuznetsova, No. 17 Francesca Schiavone, No. 21 Magdalena Maleeva, No. 23 Fabiola Zuluaga.