When President Carter landed here tonight, he was greeted by the most politically troubled yet intriguing and important leader in the East European bloc - Polish Communist Party chief Edward Gierek.

Gierek is important simply because he has, for the past seven years, managed to hold onto power in a country with 35 million of the most expressive and independent-minded people in the Soviet-led Warsaw Pact.

Yet he is becoming potentially more important, more intriguing and, at the same time, possibly even more vulnerable, politically, because in the past few months he has moved onto a new course that is rare for Communist leaders outside the Soviet Union.

Carter is the fourth foreign leader to visit Gierek in three months. He was preceded here by the shah of Iran, West German Chancellor Helmut Schmidt and the king of Belgium.

During that period, Gierek also traveled to France for a meeting with President Valery Giscard d'Estaing, to Italy for a meeting with Premier Giulio Andreotti and a meeting with Pope Paul VI, and to Moscow where he was given first-class treatment - including a meeting with Soviet President Leonid Brezhnev.

What all this means is not yet clear. There are two schools of thought.

One is that Gierek, 64, is using international forays to help bolster his sagging image at home, for Gierek has serious political troubles.

The Polish economy is some $12 billion in debt to the West Polish agriculture has suffered grave setbacks. A severe meat shortage persists, as do the long lines in front of butcher shops. There is a shortage of grain, of housing and consumer goods.

An attempt to raise meat prices by 60 per cent last year resulted in workers' uprisings reminiscent of those that toppled governments here twice in the past two decades.

Gierek, in effect, has lost the ability to really govern, and Poles - though they appear to still like him as an honorable and decent man - seem to understand that the government is stalemated.

In an interview yesterday, the candid Polish leader acknowledged that he had given up hope of trying to raise meat prices at least for "the near future."

Whenever such a decision is taken, he added, it would "have to be based on the firm conviction that it would be acceptable to the public."

Thus, Gierek's international diplomacy is seen as an attempt to improve his status among Poles, and, at the same time, convince Western leaders that he must be extended more credit - and more patience in terms of repayment - if he is to keep the lid on his country, and to remind the Soviets just how difficult a situation he faces.

The other school of thought about Gierek's travels combines an element of this view, since there is no argument among Polish observers that Gierek is seeking both domestic political and economic gains in his international diplomacy.

In addition, one Warsaw journalist observed, "there is the feeling that Gierek really does want to become an internationally known statesman. He'd like to be a Giscard d'Estaing or a Helmut Schmidt. He is a former coal miner, not an intellectual and he can't fight his way out of a paper bag on economic subjects. But people like him. The leaders he meets with all seem to like and respect him."

"He also may feel, another adds, "that he can serve as someone who can carry the banner of East-West detente more easily, who can go beyond what is possible for the Soviets to do in this field."

Indeed, in discussing the Carter visit in yesterday's interview, Gierek chose to emphasize the important international issues that he wanted to raise with the President.

Unlike most other East European Communist leaders, Gierek spent many years in the West. His family migrated to France, in 1931, that he first joined the Communist Party.

He later fought in the Belgian resistance, returning to Poland in 1948.

Further evidence of Gierek's desire to become a statesman is seen by many foreign observers in the extraordinary meeting that he held here in late October with Stefan Cardinal Wyszynski, the leader of Poland's Catholic church and probably the most popular man in this country. This was followed in November by his meeting with the Pope.

Gierek needs the church as a stalizing force to be kept from getting out of hand.

Here, too, many believe there may be more to it than that, because Gierek's unusual meetings with the church leaders have hurt the Polish leader with some Communist Party hard-liners who don't want to see any accommodation with the church.

In this view, Gierek is credited with being a risk-taker, nationalist and statesman - not simply an opportunistic Communist official - in understanding that a measure of conciliation with the church is in the national interest of a country where almost 90 per cent of the population is Catholic.