Geodesic
On absolute and unconditional convergence of series in the general Franklin system
Izvestiya. Mathematics , Tome 73 (2009) no. 2, pp. 279-300.

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We prove that, for any admissible sequence, the corresponding general Franklin system $\{f_n(x)\}_{n=0}^{\infty}$ possesses the following property. A series $\sum_{n=0}^{\infty}a_nf_n(x)$ is absolutely convergent almost everywhere on a set $E$ if and only if it is unconditionally convergent almost everywhere on $E$.
Keywords: series, general Franklin system, absolute convergence, unconditional convergence. 
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G. G. Gevorkyan; K. A. Kerian. On absolute and unconditional convergence of series in the general Franklin system. Izvestiya. Mathematics , Tome 73 (2009) no. 2, pp. 279-300. http://geodesic.mathdoc.fr/item/IM2_2009_73_2_a1/

[1] B. S. Kashin, A. A. Saakyan, Ortogonalnye ryady, 2-e izd., Izd-vo AFTs, M., 1999 ; B. S. Kashin, A. A. Saakyan, Orthogonal series, Transl. Math. Monogr., 75, Amer. Math. Soc., Providence, RI, 1989 | MR | Zbl | MR | Zbl

[2] E. M. Nikishin, P. L. Ulyanov, “Ob absolyutnoi i bezuslovnoi skhodimosti”, UMN, 22:3 (1967), 240–242 | MR

[3] G. G. Gevorkyan, “Absolute and unconditional convergence of series in Franklin systems”, Math. Notes, 45:3 (1989), 200–210 | DOI | MR | Zbl

[4] G. G. Gevorkian, H. L. Mikayelyan, “Unconditional and absolute almost everywhere convergence of series by the general Franklin system”, J. Contemp. Math. Anal., 34:3 (1999), 10–25 | MR | Zbl

[5] G. G. Gevorkyan, A. Kamont, “Unconditionality of general Franklin systems in $L^p[0,1]$, $1

\infty$”, Studia Math., 164:2 (2004), 161–204 | DOI | MR | Zbl