Geodesic
On the Fourier–Haar Coefficients of Functions of Several Variables with Bounded Vitali Variation
Matematičeskie zametki, Tome 70 (2001) no. 6, pp. 803-814 
S. Yu. Galkina. On the Fourier–Haar Coefficients of Functions of Several Variables with Bounded Vitali Variation. Matematičeskie zametki, Tome 70 (2001) no. 6, pp. 803-814. http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a0/
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     author = {S. Yu. Galkina},
     title = {On the {Fourier{\textendash}Haar} {Coefficients} of {Functions} of {Several} {Variables} with {Bounded} {Vitali} {Variation}},
     journal = {Matemati\v{c}eskie zametki},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we study the behavior of the Fourier–Haar coefficients $a_{m_1,\dots,m_n}(f)$ of functions $f$ Lebesgue integrable on the $n$-dimensional cube $D_n=[0,1]^n$ and having a bounded Vitali variation $V_{D_n}f$ on it. It is proved that $$ \sum _{m_1=2}^\infty\dotsi\sum _{m_n=2}^\infty |a_{m_1,\dots,m_n}(f)| \le\biggl(\frac{2+\sqrt 2}3\biggr)^n\cdot V_{D_n}f $$ and shown that this estimate holds for some function of bounded finite nonzero Vitali variation.

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