Abstract
The article focuses on the problem of basis property for the Jacobi polynomial system \(P_n^{\alpha ,\beta }(x)\) in the weighted variable exponent Lebesgue space \(L^{p(x)}_\mu ([-1,1])\). The sufficient, and in a certain sense, necessary conditions on the variable exponent p = p(x) > 1 ensuring the uniform boundedness of Fourier-Jacobi sums \(S_n^{\alpha ,\beta }(f)\) (n = 0, 1, …) with − 1 < α, β < −1∕2 in \(L^{p(x)}_\mu ([-1,1])\) are obtained.
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Shakh-Emirov, T.N., Gadzhimirzaev, R.M. (2021). The Convergence of the Fourier–Jacobi Series in Weighted Variable Exponent Lebesgue Spaces. In: Kusraev, A.G., Totieva, Z.D. (eds) Operator Theory and Differential Equations. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-49763-7_16
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DOI: https://doi.org/10.1007/978-3-030-49763-7_16
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