Geodesic
On the recovery of the coefficients of a rearranged Haar series
Sbornik. Mathematics, Tome 58 (1987) no. 1, pp. 31-57

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The author has previously established that, for any rearrangement of a Haar series, if the rearranged series converges everywhere on $[0,1]$ to a bounded function $f(x)$ then the coefficients of the series can be recovered from the sum $f(x)$ using the formulas of Fourier; however, no analogous assertion holds, in general, for an arbitrary summable function $f$. Generalizing his previous results, the author shows, in particular, that the theorem on the recovery of the coefficients of a rearranged Haar series goes over to functions of the class $L_2$, but not to the class $L_p$ for any $p2$. Bibliography: 9 titles. 
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     title = {On the recovery of the coefficients of a rearranged {Haar} series},
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G. M. Mushegyan. On the recovery of the coefficients of a rearranged Haar series. Sbornik. Mathematics, Tome 58 (1987) no. 1, pp. 31-57. http://geodesic.mathdoc.fr/item/SM_1987_58_1_a2/