The Stability of Wavelet-Like Expansions in A∞ Weighted Spaces

We prove L-p boundedness in A(infinity) weighted spaces for operators defined by almost-orthogonal expansions indexed over the dyadic cubes. The constituent functions in the almost-orthogonal families satisfy weak decay, smoothness, and cancellation conditions. We prove that these expansions are stable (with respect to the L-p operator norm) when the constituent functions suffer small dilation and translation errors.