Who is this guy Gannon?" a puzzled Gov. Edmund G. (Jerry) Brown Jr. asked the other day. "Isn't he supposed to be a liberal? Bill Loeb has been a lot fairer to me than he has."

Loeb is the arch-conservative publisher of the Manchester, N.H., Union Leader, for decades a scourge of presidential candidates who didn't share his views. Gannon is James P. Gannon, executive editor of the Des Moines Register, which is sponsoring two presidential debates in Iowa, one for each of the major parties.

Brown desperately wants to get into the Jan. 7 Democratic debate with President Carter and Sen. Edward M. Kennedy (D-Mass.), but Gannon won't let him. Brown, he says, hasn't shown he is making a genuine effort to compete for delegates at the Iowa precinct caucuses Jan. 21.

Brown is used to having his way with the press, but the paper Gannon edits is anything but pliable. The Regiter's success in framing the public debate in Iowa, and in setting the agenda for politicians, home-grown as well as visiting, has few equals in the nation's political-journalistic power pageant.

All of this outrages Brown, who until a week ago has shown no interest in campaigning in Iowa. The Register, he has said, has imposed a "gag rule" and violated his First Amendment rights of free speech.

"I'm troubled by this concept that in a free society that I have to convince an editor that I'm a bona fide candidate. I am running for president," he said in a television interview during his first-ever trip to Iowa Tuesday. "I'm raising funds in every state. I've traveled as far as I can, and for one human being to somehow say I'm not a real candidate is a very dangerous turn of events."

These are fighting words for any editor. And they've caused Gannon and his respected newspaper no end of trouble. Scores of people from around the country have written letters of protest. New Republic magazine has accused the paper of perpetrating an "Iowa Brownout." And even the Register's humor columnist, Donald Kaul, has suggested his paper is making a big mistake.

"Give us a break, boss," he said in a column Sunday. "Maybe he will bring Linda Ronstadt with him."

How did Gannon get into a mess like this? Until 18 months ago, he was a highly regarded Washington reporter for the Wall Street Journal, a graceful writer, the classic mildmannered newsman, fair, middle of the road. "He is the closest you can get to being a Boy Scout without being boy scoutish about it," says one friend.

It all started over a breakfast of cornflakes (what else in Iowa?) with his wife Joan, Gannon recalls. "We were talking about all the candidates and she said, 'Why don't you get them all together for a debate?'" Gannon, who sat on the press panel for the first Carter-Ford debate in 1976, thought it was a "terrific" idea. "So I started writing letters," he said.

His first batch went out Aug. 10. The response from the heavyweights in the Republican field was lukewarm at best. There was no word at all from the Carter White House. Then, during an interview with Kennedy before he announced his candidacy, Gannon asked him if he'd be willing to participate in a debate in Iowa. Kennedy was noncommittal, but didn't rule it out.

On Nov. 6, the day before Kennedy formally announced, Gannon received a call from White House press secretary Jody Powell. "You've got an interesting idea there," Powell said, according to Gannon.

Carter promptly challenged Kennedy to a debate. Kennedy accepted. Suddenly, everyone developed a burning interest in the Iowa debates. Brown, who hadn't been invited, said he wanted to be part of the debates. And a week ago Friday, the California governor told a group of reporters in Washington that he had decided to campaign in Iowa.

Reminded that his aides had repeatedly said he wouldn't campaign in Iowa, Brown aid, "My people have to say that kind of thing just to make conversation with you guys."

The Register was not impressed. Brown, it said in an editorial, had found "a sudden love for Iowa."

"We have no interest in 'gagging' Brown," it said. "We have, in fact, tried since August to get him to give us a phone interview which we offered to transcribe and run on the editorial page. Brown said he was interested but he never could find the time."

"If Brown wants to debate in Iowa, he must first show that he intends to make a genuine effort to compete for delegates in the caucuses," the editorial concluded.

Brown will have a chance to prove to Iowa -- or at least the Register -- that he means business on Nov. 29, when he is scheduled to meet with the paper's editorial board.

While it may strike outsiders as odd that a paper in Iowa should be involved in a controversy like this, "it is also absolutely typical that the Register should be in the middle of it," says Paul Engle, for decades the director of the respected Iowa Writers Workshop at the University of Iowa. "In a certain sense, the Des Moines Register is the state of Iowa."

"Editors of the Register have never been afraid to take a firm stand," Engle continues. "It's part of what I view as the most unusual experience of living in Iowa."

With a daily circulation of 220,000 and a Sunday circulation of 410,000, the Register is the only Iowa paper with a statewide circulation, and it dominates the flow of news and information in the state in a way that few regional newspapers do.

It is also a rather cosmopolitan paper, though published in large part for a small town audience. Sprightly written, the Register appears to regard itself as a beacon of enlightenment in the cornfields. The tension between content and readership makes for a paper both loved and hated.

Owned since 1903 by the Cowles family, the Register publishes an uncommon amount of national and international news for a paper in its location. With award-winning reporters like James Risser, Nick Kotz, Clark Mollenhoff and Richard Wilson, its Washington bureau has long maintained a high profile in the nation's capitol. Altogether, the paper has won 13 Pulitzer Prizes, a total few papers can match.

Yet the Register's bread and butter has always been Iowa. It is an unabashed booster for the state. It is for the family farm, environmental protection, clean government, and Iowa arts, perhaps more so than many people in the state would like.

Engle gives an example. He tells of being introduced by his first wife, an Iowa native, to another woman. The woman asked Engle what he did for a living. When he told her he was a poet, she replied, "Oh, I'm so sorry."

"The Register takes the opposite view," says Engle. "It says, 'Paul is a poet. That's fine. We need people like that.' It's been a humanizing progressing influence on the state."

Editorially, the Register is "an independent newspaper," which until recent years, when it has given its blessing to Democrats the likes of Sens. John Culver, Dick Clark and Harold Hughes, tended to be more Republican than anything else.

But its most important role, in the view of many, has been its ability to set the state's political agenda. It covers politics exhaustively, and seldom does a presidential candidate go anywhere in the state without a Register reporter on his tail. Politicians and out-of-state reporters court and seek counsel from the paper's colorful political writer, James Flansburg. aIts sometimes controversial Iowa poll is the yardstick by which candidates are judged between elections.

"They think they're very important in state politics. Their detractors don't think so," says state Republican Chairman Stephen Roberts. "They fancy themselves the best, the trend setters. They tend to be a little liberal, and they don't have much sympathy with conservatives."

"Witness Roger Jepsen [the state's new Republican senator]," adds Roberts. "They went after him with a vengance, and after he beat Dick Clark they wrote an editorial on how 'the best man lost'."

With the Iowa precinct caucuses becoming the first test of strength in the presidential race, the Register has taken on an influence felt far beyond the borders of Iowa. Tim Kraft, Carter's campaign manager, has frequently said that what the Register wrote about Carter, while still an obscure former Georgia governor was more important to his early surge in 1975 and 1976 than anything written in Washington or New York.

That's what makes Jerry Brown's current controversy all the more fascinating.

Admirers of the paper, like Herbert Strentz, chairman of the journalism deportment at Drake University in Des Moines, are betting that Brown eventually will be allowed into the debate.

"I guess Jerry Brown will just have to do some penance for a while and prove he loves Iowa," says Strentz. CAPTION: Picture 1, JAMES P. GANNON; Picture 2, GOV. EDMUND G. BROWN