Geodesic
On the rate of approach to zero of the coefficients of null series in the Haar and Walsh systems
Izvestiya. Mathematics , Tome 11 (1977) no. 3, pp. 665-676

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The existence of null series in the Haar system with coefficients approaching zero at any prescribed rate admissible for such series is proved, and a class of null series in the Walsh system with coefficients tending to zero sufficiently rapidly is also constructed. It is proved that the series of squares of coefficients of a null series in the Walsh system may diverge arbitrarily slowly. Bibliography: 6 titles. 
@article{IM2_1977_11_3_a9,
     author = {V. A. Skvortsov},
     title = {On the rate of approach to zero of the coefficients of null series in the {Haar} and {Walsh} systems},
     journal = {Izvestiya. Mathematics },
     pages = {665--676},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {1977},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1977_11_3_a9/}
}
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V. A. Skvortsov. On the rate of approach to zero of the coefficients of null series in the Haar and Walsh systems. Izvestiya. Mathematics , Tome 11 (1977) no. 3, pp. 665-676. http://geodesic.mathdoc.fr/item/IM2_1977_11_3_a9/