THE MALTA SUMMIT : For Gorbachev, Image of Warmer U.S. Ties Is a Plus : Diplomacy: The Soviet people see improved superpower relations as boosting their chances for better living conditions, Kremlin aides say.

For Soviet President Mikhail S. Gorbachev, the first payoff from his weekend summit with President Bush came when they sat down Sunday afternoon for the first joint press conference by U.S. and Soviet leaders in more than four decades of such summits.

The message that the televised press conference sent back to viewers in Moscow was that Soviet-American relations are on a new basis--friendlier, more cooperative and no longer confrontational.

Significant progress was made, the two leaders said, in defining the issues and setting the timetables necessary to conclude a series of arms control treaties, including an agreement that will reduce strategic arsenals by as much as 50%.

This was No. 1 on Gorbachev’s agenda for the summit, and Soviet officials said that Moscow’s hopes for the meeting were justified.

“We had the feeling before that we must start moving in our relationship, and now we know that the American side shares this,” Georgy A. Arbatov, director of the Soviet Institute for the Study of the United States and Canada, said here Sunday. “From this meeting, we know that we have the basis for moving ahead with the United States and going faster. The understandings are there.”

The United States, responding to the Soviet Union’s serious economic problems, had also offered to begin immediate negotiations on a trade agreement, to extend the lower tariffs of most-favored-nation trading status to Moscow and to support Soviet membership in such key international economic organizations as the General Agreement on Tariffs and Trade.

“Bush has signaled an end to U.S. economic warfare against the Soviet Union,” Arbatov said. “This is important for our economic development and our integration into the world economy.”

And the two presidents’ intense discussions on Eastern Europe, where developments continue to race beyond the superpowers’ ability to predict, led to a broad measure of understanding, Bush and Gorbachev said, on what is now Moscow’s most sensitive foreign policy worry.

Perestroika , in short, appeared to be paying off in significant ways, and although the immediate results were in foreign affairs, they offered some much-needed hope for Soviet citizens who feel increasingly trapped in their country’s deepening economic crisis.

In the Soviet public consciousness, better Soviet-American relations translate into reduced government spending on defense, more money available for consumer goods, less of the privation that people have known for generations, greater prospects for foreign trade and high-quality imports, less tension in international affairs and more freedom in domestic politics.

“Soviet-American relations have become one of those barometers of well-being that people keep track of,” Leonid I. Dobrokhotov, a foreign policy specialist from the Soviet Communist Party’s Central Committee, said. “They know that when Soviet-American relations go bad, things can really turn sour for them, and they hope that, as relations become better, life will get sweeter--at least a little bit sweeter.”

Bush, with Gorbachev at his side, reinforced this message at the press conference with praise of the Soviet president and perestroika , or restructuring, as Gorbachev’s five-year-old program of political and economic reforms is known.

“There is enormous support in our country for what Chairman Gorbachev is doing inside the Soviet Union,” Bush said, describing Soviet-American relations as “improving dramatically.” “There is enormous respect and support for the way that he has advocated peaceful change in Eastern Europe.”

And a key Gorbachev foreign policy adviser, recalling British Prime Minister Margaret Thatcher’s early characterization of Gorbachev, said of Bush, “This is a man we can do business with.”

The summit, proposed by Bush but long sought by Gorbachev, had become, in the short month since it was first announced, an important test of the ability of the Soviet leader’s foreign policy to bring practical results, not just applause from abroad.

“In the West, it is often said that Gorbachev tries to substitute foreign policy successes for the lack of progress in his reforms at home,” a senior Soviet commentator said here Sunday, “and there is a kernel of truth in that. People do wonder what they themselves get out of these enthusiastic welcomes he gets abroad. . . .

“Nobody is going to eat better tomorrow as a result of these talks with Bush, and nobody expects to. What people are looking for are results, something that goes beyond the cheers of ‘Gorby, Gorby.’ In arms reduction, there is a promise of that, and in economic cooperation and trade, there is more than just a promise of it.”

After a hard look at what Bush had laid out in the first and the most important round of talks, Gorbachev’s top advisers concluded that Soviet-American relations are developing very much on track, headed in the direction Moscow had hoped for and gathering speed.

“The summit demonstrated that movement has resumed between Moscow and Washington,” Arbatov said. “We had this long pause at the start of the Bush Administration. We accept that this was due more to technical than political reasons, but it did leave us uneasy.

“Now, we know that we will move ahead in all important fields--arms control, economic cooperation, international questions, regional issues, bilateral relations.”

In arms control, what was most important, Soviet officials said, was the agreement to identify key issues and set a timetable for their resolution so that a treaty reducing nuclear arsenals is ready in all major aspects by the next summit in late June and a multilateral convention reducing conventional armed forces in Europe is completed by the end of 1990.

Secretary of State James A. Baker III is due to travel to Moscow in January for talks with Foreign Minister Eduard A. Shevardnadze on the first set of issues, and one or two other meetings are likely before the June summit.

Although Washington had already declared its desire for an agreement next year on reducing conventional forces in Europe, Moscow was pleased by Bush’s personal commitment to resolve the differences among the North Atlantic Treaty Organization’s 16 members that have slowed progress in negotiations between the Atlantic Alliance and the seven countries of the Warsaw Pact.

U.S. acceptance in principle of a European summit meeting, with its participation and that of Canada, surprised Soviet officials, though it is uncertain whether it would be convened for the signing of the conventional arms agreement or later on a broader basis to discuss the Continent’s future.

Bush’s offer to end production of all chemical weapons in return for matching Soviet and Third World concessions also won cautious praise from specialists in the Soviet delegation.

“Arms control for us is perhaps the touchstone of the whole Soviet-American relationship, and we were pleased not only by what Bush said but by the effort he took to address our concerns and priorities,” a Soviet foreign policy specialist remarked.

Gorbachev, addressing the press conference aboard the Soviet cruise ship Maxim Gorky, said there had been “elements of optimism and pessimism” in Moscow’s pre-summit assessment of the prospects for Soviet-American relations but that the elements had been “cautious and restrained.”

“Now that the meeting has taken place, and we have summed up the results, together with (President Bush), I can tell you that I am optimistic about the results and the prospects that are open now,” he said.