Littlewood-Paley decomposition in quantum calculus

摘要

We introduce Littlewood-Paley decomposition related to q-Rubin's operator, this allows us to provide a dyadic characterization of Sobolev, Holder and Lebesgue spaces associated with the q-Rubin's operators and to establish some embedding results for these spaces. We construct the paraproduct operators associated with the q-Rubin's operators and we establish its action on the Sobolev and Holder spaces.