Despite significant federal limitations on the city's still-young form of home-rule government, District of Columbia Democratic voters believe overwhelmingly that the person they choose as mayor can make a difference in a wide range of matters affecting their lives, according to a Washington Post Poll.

The Post poll of 1,020 Democrats indicates that, as the city prepares for the Sept. 12 primary election, voters think - by margins ranging from 67 percent to 91 percent - that a mayor can control or exact influence on such problems as honesty and efficiency in government, race relations, providing jobs for youths and holding down rent and taxes.

Furthermore, their perceptions of which candidates are best able to cope with particular problem areas emerge as possibly a key factor in what now appears to be a very closely contested election campaign.

The poll showed that in overall voter preference, City Council Chairman Sterling Tucker holds a narrow lead, getting 24 percent compared to 20 percent for incumbent Mayor Walter E. Washington and 18 percent for council member Marion Barry.

But otherwise hidden strengths and weaknesses emerge for each candidate when voters are asked to compare them on their ability to handle specific problems.

For example, while Barry places a poor third overall among blacks polled, he does slightly better than his two major opponents among blacks as the one candidate who could provide jobs for young people - a vital concern here.

Barry also does exceedingly well on that jobs issue among a possible swing group in the electorate - blacks who have not made up their mind on whom to support.

At the same time, the poll indicates, while Barry has been emphasizing government efficiency in his campaign, those polled consider him the weakest of the three in the ability to provide efficient city services. Even many of Barry's supporters defect to other candidates in that area.

Respondents in the Post poll were given a list of 13 city problem areas and told "Some people say that a mayor can influence almost every aspect of city life; others say that certain problems will remain the same no matter who is mayor. Here are some city problem areas; for each please tell me if you feel a mayor can or cannot make much difference in coping with that problem." Those who said a mayor could make a difference on an issue were then asked which candidate they felt could handle that issue best.

Earlier studies elsewhere, including several by The Washington Post, indicate that a key difference among those who vote and those who do not is the way they regard the power of political officeholders to influence the issues of the day. In adidtion, those who vote generally are more affluent and more educated than nonvoters.

The Post poll, which focuesed on people who had voted at least once in the last 10 elections, conforms with these findings. For example, although about half the people who live in the city are renters, the poll indicates that three-fourths of the Democratic voters sampled own their homes. Similarly, 77 percent of the city's population is black, but only 70 percent of the random sample of voters interviewed were black.

The poll indicates that blacks and whites have similar attitudes about what a mayor can accomplish, for the most part. Whites, however, are more confident of a mayor's ability to exert influence or control over race relations and honesty in government. Blacks are more confident of a mayor's ability to help prevent housing displacement and to hold down rents and utility bills.

Sentiment about what a mayor can do was nearly identifical across the city, except in Ward 3, the predominantly white and affluent section west of Rock Creek Park, and in Ward 8, the poverty-ridden and mostly black. Anacostia section of Southeast Washington.

Ward 3 residents felt more strongly that a mayor could provide honest government and maintain a healthy racial climate. Anacostia voters generally were less confident than all others in the ability of a mayor to solve most city problems except for rent levels, where they were above average in their belief that a mayor can make a difference.

Respondents were not asked to say which concerns were uppermost in their minds, so the answers cannot be considered a measure of the relative importance of any particular issue in the election.

In some instances, there is a sharp difference in the way the candidates are perceived and the way they are conducting their campaigns. This is true, for example, in the case of Barry and the issue of jobs for the young.

Barry is the former executive director of Pride Inc., which helped to provide job training for hard-core unemployed youths, Several persons interviewed in person felt that Barry would be best at finding jobs for the young because of his past work at Pride. Thirty percent, overall, considered Barry best to solve this problem as compared to 21 percent for Tucker and 20 for Washington, who has emphasized his efforts to obtain a job corps traning program for the city.

Although Barry mentions his work at Pride as evidence of his ability to work with hard-core unemployed youth, he does not emphasize any ability of this own to find jobs for such people.

Instead, in what he acknowledges as an attempt to broaden his base, he has been playing up his role as chairman of the council's finance and revenue committee and liaison to the politically influential business sector.

The disproportionate support for Barry on jobs for the young strengthents his potential in wards 4, 7 and 8 - wards in which he is trailing badly overall. Among the people undecided on their choice for mayor, more than half those polled believe a mayor can make a difference in the area of youth jobs, and about half of those believe Barry is the man.

Voter perceptions of the issue of keeping a lid on rents appear to be in sharp contrast to the recent history of rent control here. Tucker, the person most publicly associated with a successful effort to allow landlords increases of 2 percent to 10 percent, is the candidate seen as best able to keep rents down. Washington, who initially vetoed legislation allowing these increases, does worst.

Washington does not do well in two areas he has placed heavy emphasis on thus far - his ability to get maximum aid from Congress for the city and to maintain a healthy racial climate in the city.

The largest portion of those interviewed - 35 percent - is still undecided on a choice for mayor. The way those people perceive the ability of the candidates to cope with certain problems could be a decisive factor in the race.

When those polled were asked if they felt city services such as police protection and trash pickup in their neighborhoods were better, worse or the same as in other areas, 28 percent answered better, 18 percent responded worse and 44 percent felt services were the same.

The sharpest differences, once again, were in Ward 3 and Ward 8. In Ward 3, more than other part of the city, residents felt the services were as good or better than services offered to residents elsewhere in the city. Respondents in Ward 8, by contrast, in keeping with past patterns, felt more than residents elsewhere that they did not get their share of services.