JERUSALEM — Even the Palestinian Kassam rocket launchers took time out when Israeli Prime Minister Ariel Sharon was hospitalized: Either they were preparing for the Muslim holiday of Id al-Adha, or they were saying, let’s wait and see.

The Kassam rockets were back in action this week. They didn’t hit anyone, but they did indicate that Sharon’s absence from the decision-making process has not changed the patterns of conflict — at least not until Jan. 25 elections for the Palestinian legislature.

In any case, Palestinian society appears too consumed by its own internal problems to worry too much about Sharon’s condition, and what will come next.

Most Arab reaction to the debilitating stroke Sharon suffered Jan. 4 has referred to his bloody past, underplaying his historic withdrawal of Jewish settlements from the Gaza Strip last summer.

Even the Web page of Al-Jazeera — which, like all major Arab television networks, has been broadcasting live reports from the Jerusalem hospital where Sharon is hospitalized — contained an article saying Sharon “the butcher, sometimes the Butcher of Beirut, sometimes the Butcher of Palestine, is rarely mentioned without listing

the dozens of crimes he committed and the thousands of Arabs he killed. “

Palestinians remember Sharon foremost for the 1953 anti-terror reprisal he led in the West Bank village of Kibya in which 69 Palestinians, including many civilians, were killed; for having orchestrated the 1982 Lebanon War to destroy the PLO’s terror enclave in southern Lebanon; for having failed to prevent the Christian massacre of Palestinians in the Sabra and Shatila refugee camps in Beirut; and for his role as the architect of the Israeli settlement movement in the territories.

One of the few public voices to criticize Sharon’s demonization was Knesset Member Abdulmalik Dehamshe of the Islamic-oriented United Arab List.

“I have opposed Sharon for many years, and I have said harsh things to him, ” Dehamshe told Ha’aretz, “but who would have thought that this man would withdraw from Gaza?”

Another local voice of sympathy was that of Talal al-Krinawi, mayor of the Bedouin town of Rahat, which is located close to Sharon’s Sycamore Farm in the Negev.

“If you had told me to vote Sharon before 2001, I would have preferred to amputate my arm,” Krinawi told Yediot Achronot’s Ynet Web site.

Ahead of the March 28 elections, however, “I would have proudly urged everyone to vote for him in the elections,” he said. “I and many other Arabs love him very much. We had our hopes pinned that he would lead us to peace.”

Indeed, some Israeli Arabs interviewed in the Israeli press shortly after Sharon’s stroke said that despite the public Arab criticism of Sharon, many Israeli Arabs privately considered Sharon “a real man,” whose word could be trusted.

The conspicuous element in Arab reaction over the past few days has been the absence of public rejoicing over Sharon’s ailment, unlike after Sharon’s first stroke in December.

Official Palestinian Authority reactions were restrained, reflecting puzzlement.

The P.A.’s deputy prime minister, Nabil Sha’ath, said it was too early to tell whether Israelis “would return to the right.”

“We are interested in the peace process,” said Prime Minister Ahmad Qurei, but Sharon’s ailment “will affect not only Israel but the entire region.”

The Arab confusion is genuine. Despite frequent criticism of Sharon, many Arabs believe he has two advantages: He broke the taboo over evacuating settlements, and he is a known entity.

Ehud Olmert, Israel’s acting prime minister, is still an enigma in a national leadership role, despite his comments in favor of further West Bank withdrawals.

Will Sharon’s Kadima Party win the elections if it is led by Olmert? Will it be strong enough to push through withdrawals from the West Bank?

“There is widespread concern among Palestinians that with this sudden absence of Sharon from political life, newly emerging Israeli leaders will simply rush to compete with each other over who can be tougher with the Palestinians, to boost their popularity ahead of the upcoming Israeli elections in March,” Hisham Ahmed, a political science professor at Bir-Zeit University near Ramallah, wrote on the joint Palestinian-Israeli Web page Bitterlemons.

With Sharon “it was bad, and with other” Israeli prime ministers “it will be bad,” said Dr. Mustafa Barghouti, a human rights activist running for the Palestinian Legislative Council. “Unless we see a government of Israel that ends the occupation, we won’t see change.”

Israeli security experts warned this week that the various Palestinian terrorist groups might try to provoke Israel to see how Olmert reacts. Defense Minister Shaul Mofaz told the Cabinet on Sunday that the army was on high alert in case Hezbollah tried to attack northern Israel.

Former Mossad head Ephraim Halevy said an interview that Olmert would react “strongly” to any attack in order to stabilize his image in the Arab world.

On the other hand, now that the issue of voting in eastern Jerusalem seems to have been resolved — Mofaz declared Tuesday that Palestinians in eastern Jerusalem would be allowed to vote, just as they had in past Palestinian elections — some analysts believed that none of the major political powers in the Palestinian territories would risk an escalation.

Moreover, the Palestinians are so preoccupied with their own internal disarray that they have little energy to devote to the challenge of a new Israeli leadership. Having ignored advice not to further expand its huge employment rolls, the Palestinian Authority now is nearly bankrupt, and it may not be able to pay salaries next

month. It faces a huge budget deficit and has done little to tame rival militias fighting each other in the streets of the Ghassan Khatib, the P.A. planning minister, sought to blame Sharon for the “continuous shift in the internal Palestinian balance of power in favor of the extremists.”

In an article this week on Bitterlemons he charged that Sharon’s “use of force” legitimized the use of force by Palestinian hardliners and made it “impossible” for a Palestinian “peace camp” to convince the public of its way.

Some in the Palestinian Authority advocated postponing elections until the situation in Israel stabilized and internal Palestinian anarchy cooled down. But jailed Fatah movement leader Marwan Barghouti warned against using Sharon’s health as a pretext to postpone the Palestinian election.

P.A. President Mahmoud Abbas said that he also saw no reason why Sharon’s demise should lead to a postponement of the election.

“The election is a national Palestinian issue and it must not be linked to any foreign concerns, such as what is happening in Israel with Sharon,” Barghouti said.