Geodesic
Unconditional convergence for wavelet frame extensions
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 45, Tome 456 (2017), pp. 135-143 
E. A. Lebedeva. Unconditional convergence for wavelet frame extensions. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 45, Tome 456 (2017), pp. 135-143. http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a10/
@article{ZNSL_2017_456_a10,
     author = {E. A. Lebedeva},
     title = {Unconditional convergence for wavelet frame extensions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {135--143},
     year = {2017},
     volume = {456},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a10/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $\{\psi_{j,k}\}_{(j,k)\in\mathbb Z^2}$, $\{\widetilde\psi_{j,k}\}_{(j,k)\in\mathbb Z^2}$ be dual wavelet frames in $L_2(\mathbb R)$, let $\eta$ be an even, bounded, decreasing on $[0,\infty)$ function such that $$ \int_0^\infty\eta(x)\ln(1+x)\,dx<\infty, $$ and $|\psi(x)|,|\widetilde\psi(x)|\le\eta(x)$. Then the series $\sum_{j,k\in\mathbb Z}(f,\widetilde\psi_{j,k})\psi_{j,k}$ converges unconditionally in $L_p(\mathbb R)$, $1.

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