UNDER BRIGHT skies, Sharon Pratt Dixon took office as mayor yesterday, evoking the best of a Washington that she grew up in -- and that she grew up loving. She seemed uncowed by the challenges of the hour -- drugs and crime, mounting financial pressures and racial polarization. Instead, Mayor Dixon spoke of what she believes is "the strength that abides in Washington, D.C.": the cultural heritage and moral values that were part of the community in which she was "reared, disciplined and loved" by family members and by a home-room teacher at Roosevelt High School who encouraged her "to pursue my dreams." Striking a chord with longtime residents from every neighborhood, the new mayor recalled a time when "we were in many ways richer than we are now, for we had a sense of community, a deep commitment to one another and an uncompromising devotion to excellence."

This is the theme that would spark lively applause and set heads nodding in approval when she used it time and again in her speeches on the way to election. "Throughout the campaign you heard me say 'clean house.' And I said that it means many things. One thing it clearly means is rediscovering some time-honored values -- pulling the dust and cobwebs off of these values that were set aside too easily in the last fast-paced 'let's have-it-all' decade."

But the inaugural call of Mayor Dixon was for more than a mere nostalgic trip for hometown consumption. Washington is indeed "a community with a rich tradition," a city of "many hues and many cultures," but it is also a place desperately in need of a responsive, efficient local government that provides its citizens a sense of "quality service." Said Mrs. Dixon: "What the people of Washington want most is an honest deal." She promised to deliver it.

To succeed, her administration will need to pursue solvency, which must entail an improved financial arrangement with the federal government. However optimistic Mayor Dixon may be as she begins her stewardship, this is where the going will get rough -- and quickly. She intends to address these questions in some detail today, and what she has to say will be critical to the effectiveness of her administration and to the quality of life in the city. For now, she has created a welcome sense of confidence and determination, summed up in her inaugural slogan: "Yes, we will."