Among the economically beleaguered apartment dwellers of the San Fernando Valley, the tax revolt that roared approval of Proposition 13 last June and triggered a national movement rages on unabated - but without the slightest gain for Republicans.

Our intervieww with 79 registered, probable voters in Los Angeles County Precinct No. 1057, conducted with Pat Caddell's Cambridge Survey Research, revealed taxation and inflation as their principal concerns. Happy with the results of Proposition 13 (slashing California property taxes), they now want to cut federal income and Social Security taxes.

What's more, they are most unhappy with President Carter's handling of those economic problems and do not consider Gov. Edmund G. Brown Jr. the truest proponent of Proposition 13. That leads to this paradox: their overwhelming support for the reelection of both Brown and, in 1980, Carter.

The answer is yet another failure of Republican politics. Those 79 voters are overwhelmingly Democratic and, a rarity today, avowedly liberal. While they should be ready for capture on the tax-inflation issue, Rewpublicans have not reached them. Thus, tax-revolt ends on economic questions, failing to penerate the political realm.

Precinct No. 1057 is not the affluent stereotype of Southern California. Its $16,700 median income would be lower were it not for a fringe of high-priced homes. Most voters here live in modest apartments (mostly rental, with some condominiums). A combination of retired persons and young families, they voted about 5 percentage points more Democratic than the California total in 1974 and 1976, but precisely reflected the statewide vote for Proposition 13 last spring: 64 percent.

Our interviews (helped by experienced polltakers Phyllis Barish and Lyn Phelps) indicated quiet desperation, slightly alleviated by Proposition 13. "I felt I had to get money from somewhere," said a married 55-year-old clerical worker in explaining her vote for property-tax cuts.

Her position was echoed 37 to 24 in favor of Proposition 13 by those interviewed who actually voted in taht referendum. The reason given was invariably high taxes, not dissatisfaction with the quality of government. The opponents, all renters rather than apartment owners, voted against it not because of a desire for government services but because they feared they would not benefit through lower rents.

And not many have second thoughts. While most of those voters have detected no decline in government services, they feel by a 2-to-1 ratio that there will be cutbacks next year. Nevertheless, only one of 37 tax revolters professed a change of heart (a retired woman who complained that her rent had gone down but not far enough).

It might then be considered fatal that Jerry Brown has failed to convince Precinct No. 1057 that his somersault from opposition to the tax revolt to support for it was 100 percent pure. By more than 3 to 1, our voters gave his Republican opponent, State Attorney General Evelle Younger, better Proposition 13 marks than Brown. Yet those with an opinion favored Brown over younger, 56 to 13.

A 20-year-old housewife-secretary complained "the homeowner has too much to bear." She liked Younger's tax stand but opted for Brown: "He's a better man. He seems honest." Similarly, a 46-year-old actor told us: "Outside of being a little wishy-washy on Prop. 13, Brown is right in there working for us."

On the federal level, those liberal Democrats declared support of the Kemp-Roth 30 percent tax cut by more than 4 to 1 and backed suspension of Social Security payroll tax hikes by 3 to 1. Besides favoring those Carter-opposed steps, they overwhelmingly disapproved the president's handling of inflation and taxes (as well as national defense and the Russians); only Carter's Middle East record got an okay.

Yet, they gave him a 53-to-17 edge over Californian Ronald Reagan for president in 1980 (with 7 not voting and 2 undecided). "Carter just hasn't done anything right about inflation," snapped a 44-year-old mechanical engineer, who wants cuts in federal income taxes and considers taxation/inflation the nation's biggest issue. His choice for president in 1978: Jimmy Carter.

In short, no Republican has convinced these sun-drenched but hard-pressed Californians that he would do better than Carter. Nor has Brown's Republican foe presented himself as their economic savior. From the cramped apartments of the San Fernando Valley comes a signal that the Grand Old Party has lost its opportunity for 1978 and capturing it in 1980 will be all the more difficult.