The Walsh transform of wavelet type systems: convergence almost everywhere
Barbara Wolnik · Functiones et Approximatio Commentarii Mathematici · 2004
The main results of the paper are the following: the Fourier expansion of $f \in L_p$, $1 \lt p \lt \infty$, with respect to the Walsh transform of a wavelet type system converges a.e. to $f$ and if $f \in L_1$ then the same is true for the Cesàro means.