On the almost everywhere convergence of wavelet summation methods

Abstract

Let ψ be a rapidly decreasing one-dimensional wavelet. We show that the wavelet expansion of any L p function converges pointwise almost everywhere under the wavelet projection, hard sampling, and soft sampling summation methods, for 1 < p < ∞. In fact, the partial sums are uniformly dominated by the Hardy-Littlewood maximal function. ©1996 Academic Press, Inc.