Littlewood–Paley decomposition in quantum calculus

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.

COMMUNICATED BY:

• Zuhair Nashed

Keywords:

• q-Fourier analysis
• q-Rubin's operator
• Littlewood–Paley decomposition
• q-Sobolev spaces
• q-Hölder spaces
• paraproduct operators

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 46E35
• 43A32
• 33D15
• 33D60

Disclosure statement

No potential conflict of interest was reported by the authors.