Geodesic
Convergence of the Vall\'ee--Poussin means for Fourier--Jacobi sums
Matematičeskie zametki, Tome 60 (1996) no. 4, pp. 569-586.

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Let $f\in C[-1,1]$, $-1\alpha$, $\beta\le0$, $S_n^{\alpha,\beta}(f,x)$ be a partial Fourier–Jacobi sum of order $n$, and let $$ \begin{aligned} {\mathscr V}_{m,n}^{\alpha,\beta} ={\mathscr V}_{m,n}^{\alpha,\beta}(f) ={\mathscr V}_{m,n}^{\alpha,\beta}(f,x) \ =\frac 1{n+1}\bigl[S_m^{\alpha,\beta}(f,x)+\dots+S_{m+n}^{\alpha,\beta}(f,x)\bigr] \end{aligned} $$ be the Vallée Poussin means for Fourier–Jacobi sums. It was proved that if $0$, then there exists a constant $c=c(\alpha,\beta,a,b)$ such that $\|{\mathscr V}_{m,n}^{\alpha,\beta}\|\le c$, where $\|{V}_{m,n}^{\alpha,\beta}\|$ is the norm of the operator ${\mathscr V}_{m,n}^{\alpha,\beta}$ in $C[-1,1]$. 
@article{MZM_1996_60_4_a7,
     author = {I. I. Sharapudinov and I. A. Vagabov},
     title = {Convergence of the {Vall\'ee--Poussin} means for {Fourier--Jacobi} sums},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
     volume = {60},
     number = {4},
     year = {1996},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1996_60_4_a7/}
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I. I. Sharapudinov; I. A. Vagabov. Convergence of the Vall\'ee--Poussin means for Fourier--Jacobi sums. Matematičeskie zametki, Tome 60 (1996) no. 4, pp. 569-586. http://geodesic.mathdoc.fr/item/MZM_1996_60_4_a7/

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