Geodesic
On changes of variable that preserve convergence and absolute convergence of Fourier-Haar series
Sbornik. Mathematics, Tome 210 (2019) no. 6, pp. 783-808
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It is established that among all the differentiable homeomorphic changes of variable only the functions $\varphi_1(x)=x$ and $\varphi_2(x)=1-x$ for $x\in[0,1]$ preserve convergence everywhere of the Fourier-Haar series. The same is true for absolute convergence everywhere. Bibliography: 8 titles.
Keywords: Fourier-Haar series, changes of variable. 
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K. R. Bitsadze. On changes of variable that preserve convergence and absolute convergence of Fourier-Haar series. Sbornik. Mathematics, Tome 210 (2019) no. 6, pp. 783-808. http://geodesic.mathdoc.fr/item/SM_2019_210_6_a1/

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