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

Abstract

We prove Lp boundedness in A∞ 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 Lp operator norm) when the constituent functions suffer small dilation and translation errors.