The Stability of Wavelet-Like Expansions in $$A_\infty $$ Weighted Spaces

Abstract

We prove $$L^p$$ boundedness in $$A_\infty $$ 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.