Abstract
In this article, we examine the order of magnitude of the Yang-Fourier transforms for local fractional continuous functions on \(\mathbb {R}\) and satisfiying certain Lipschitz conditions. Furthermore, using the analogue of the operator Steklov, we construct the generalized modulus of smoothness in the fractal space \(L_{2,\alpha }(\mathbb {R})\) and we use the Yang-Fourier transforms to prove the equivalence between K-functionals and modulus of smoothness.
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Bouhlal, A., Ahmad, O. Yang-Fourier transforms of Lipschitz local fractional continuous functions. Rend. Circ. Mat. Palermo, II. Ser 72, 3891–3904 (2023). https://doi.org/10.1007/s12215-023-00869-5
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DOI: https://doi.org/10.1007/s12215-023-00869-5