Banishing Poverty: an Uphill Fight. Joblessness, crime continue to stymie progress in Miami's poor black neighborhoods. AMERICA'S UNDERCLASS

SMALL triumphs arrive even in a rising tide of trouble in the poor black ghetto. Liberty Mart - a tiny bit of thriving, job-creating civilization in the heart of a desolate Liberty City housing project - now lies in a heart-rending heap of rubble and charcoal under the subtropical sun. The Miami convenience store was torched during a night of rioting Jan. 18.

But Tom Petersen, who founded the store, has already raised more than $40,000 to rebuild it, and the fire helped galvanize support for the store in the neighborhood.

Small triumphs, however, are not turning the tide.

For two decades, poverty in America has been concentrated in urban ghettos like Liberty City, where welfare dependency, single-parent families, joblessness, crack addiction, and violent crime create what is increasingly dubbed an ``underclass.''

Mr. Petersen has been on leave from the local state attorney's office for three years trying to bring civilization and progress to Miami's worst neighborhoods. He has watched these neighborhoods continue to slip into social chaos.

People from all over the Americas - black, white, brown; those speaking Spanish, Creole, and sometimes English - use Miami as a doorway to a better life. Many arrive poor and move up.

But, puzzlingly, growing numbers in Miami's black American ghettos are backsliding socially and economically.

Is anything working in the ghetto?

``No. Nothing,'' Petersen says. ``I haven't seen anything. We haven't found the solution.''

Success stories can be found - from police with good community relations to successfully redeveloped shopping centers. But the ripples do not spread. Marvin Dunn, a psychology professor at Florida International University (FIU) and co-author of a book on the causes of Miami's 1980 Liberty City riots, says: ``We have no comprehensive strategy for the problems of the ghetto.''

Ghetto life is only a small part of the picture among blacks in the United States - well under 10 percent of whom are poor and living in ghetto neighborhoods.

The black professional class is growing, even in Miami, as much as the underclass. The trend in the 1980s of the rich getting richer and the poor getting poorer has been exaggerated among blacks.

Yet the prosperity of blacks at all economic levels and of all family types is losing ground to their white counterparts, according to the National Urban League's most recent report, the State of Black America 1989.

American blacks of the urban ghetto are not the poorest of the poor. Several studies have shown that Haitian immigrants probably are. Taken together, probably no ethnic group in America is more destitute than the Haitians.

Yet Haitians hold views of American blacks very similar to the worst stereotypes of white racists, notes Alex Stepick, an FIU anthropologist studying race relations in Miami. Haitians often see American blacks as lazy, violent, morally loose, and disrespectful of authority.

While young Haitian immigrants in Miami schools typically emulate the talk and dress of the black American ghetto, they retain a sense of moral and cultural superiority, Dr. Stepick says.

As Haitians overcome their language handicap, Stepick adds, they tend to outperform American blacks in school. These immigrants are too recent, however, to show the course of their progress.

The theories behind urban black poverty are developing along two basic themes.

The conservative theme blames welfare for creating a culture where poor women have no incentive to marry or to work, so they increasingly rear their children in a fatherless world of welfare dependency.

Another developing theme is that - ironically - racial integration has allowed stable black families to leave poor neighborhoods to the poor, without the moral example, institutional support, or job connections of upstanding black families.

The liberal theme is that lack of jobs, not welfare, has warped ghetto society away from family and the work ethic. Job opportunity would bring back marriage and constructive values.

For those who deal in a practical way with the ghetto, such as Tom Petersen, these themes are all at least partly right.

And the victim of ghetto poverty, he says - as more people from all quarters are saying these days - ``shares part of the blame.''

Why is opportunity lacking in Miami's Liberty City or Overtown, with black men idling the day away in parking lots and front yards when Nicaraguans a few miles away, many of them illegal aliens who don't speak English, manage to find jobs with more success?

From 1980 to 1987, joblessness in Dade County went down slightly among Hispanics while rising among blacks.

One common explanation is that immigrants are more pliant, exploitable workers, especially if they are illegal and vulnerable to deportation. Another is that blacks have traditionally taken the hardest, lowest-paying jobs in the economy, and often still do, but have found the route to upward mobility blocked.

Miami's Latin population, on the other hand, has created small enterprises more likely to hire family, friends, and fellow Spanish-speakers than would larger, more impersonal operations.

But none of these explanations satisfies close observers.

``Quite possibly, a lot of those people on the streets in the housing projects wouldn't take a job if it fell in their laps,'' Dr. Dunn says. Many can do better by doing worse, he notes, as thieves or drug peddlers. Others are without skills or motivation to work. This problem of welfare dependency is part of it, he adds.

Petersen puts the problem with the main federal welfare program, Aid for Dependent Children, in a nutshell: ``It's too little money, yet it's enough to keep a woman from going to work.''

At root these problems belie a widespread loss of confidence in self and in the system. Longtime welfare mothers speak of their fear and insecurity at leaving the meager but reliable comfort of the welfare rolls for a job.

``The majority are people who are afraid to step out'' into the working world, says Pam Golden, a social worker who advises the store and coordinates other social services daily. ``It's a big step.''

``It was that way for me,'' says Mary Redding, manager of Modello Mart in the Modello housing project. Ms. Redding has four children, never married, and dropped out of high school after the 10th grade. She lived on welfare until coming to work for Modello Mart a year and a half ago. Now she earns $7 an hour working 40 hours a week.

Modello Mart is one of Tom Petersen's efforts. The idea is to bring a functioning, constructive business into the projects, to bring some of the mothers gently into the work force, and to bring activity to community centers where other services are offered.

In the meantime, Modello has grown worse. Some 70 percent of the households now sell or use crack cocaine, according to Ms. Golden, who has surveyed the units. But some things have improved for some people. Cases like Mary Redding's still register as small triumphs.