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A characterization of weighted Besov spaces in quantum calculus. (English) Zbl 1332.33029
Summary: In this paper, subspaces of \(L^{p}(\mathbb{R}_{q,+})\) are defined using \(q\)-translations \(T_{q,x}\) operator and \(q\)-differences operator, called \(q\)-Besov spaces. We provide characterization of these spaces by using the \(q\)-convolution product.

MSC:
33D60 Basic hypergeometric integrals and functions defined by them
26D15 Inequalities for sums, series and integrals
33D05 \(q\)-gamma functions, \(q\)-beta functions and integrals
33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
33D90 Applications of basic hypergeometric functions
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