Haar wavelets on the Lebesgue spaces of local fields of positive characteristic
Tom 136 / 2014
Colloquium Mathematicum 136 (2014), 149-168 MSC: Primary 42C40; Secondary 42C15, 43A70, 11S85. DOI: 10.4064/cm136-2-1
We construct the Haar wavelets on a local field $K$ of positive characteristic and show that the Haar wavelet system forms an unconditional basis for $L^p(K)$, $1< p< \infty $. We also prove that this system, normalized in $L^p(K)$, is a democratic basis of $L^p(K)$. This also proves that the Haar system is a greedy basis of $L^p(K)$ for $1< p< \infty $.