Littlewood–Paley decomposition in quantum calculus. Issue 12 (9th September 2020) - Saoudi, A.; Fitouhi, A.
ABSTRACT: We introduce Littlewood–Paley decomposition related to q -Rubin's operator, this allows us to provide a dyadic characterization of Sobolev, Hölder 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 Hölder spaces.