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Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 12
128
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Articles

Littlewood–Paley decomposition in quantum calculus

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Pages 2115-2136 | Received 23 Sep 2016, Accepted 27 Nov 2018, Published online: 13 Dec 2018
 

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.

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Disclosure statement

No potential conflict of interest was reported by the authors.

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