Littlewood–Paley decomposition in quantum calculus. Issue 12 (9th September 2020)

• Record Type: Journal Article
• Authors: Saoudi, A.; Fitouhi, A.
• Is Part Of: Applicable analysis. Volume 99:Issue 12(2020)
• Page Start: 2115
• Page End: 2136
• Publication Date: 2020-09-09
• Subjects: Zuhair Nashed; q-Fourier analysis -- q-Rubin's operator -- Littlewood–Paley decomposition -- q-Sobolev spaces -- q-Hölder spaces -- paraproduct operators; 46E35 -- 43A32 -- 33D15 -- 33D60; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1555321
• Languages: English
• ISSNs: 0003-6811

Abstract

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.