Geodesic
Wavelets and Bidemocratic Pairs in Weighted Norm Spaces
Matematičeskie zametki, Tome 104 (2018) no. 4, pp. 527-538.

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A complete characterization of weight functions for which the higher-rank Haar wavelets are greedy bases in weighted $L^{p}$ spaces is given. The proof uses the new concept of a bidemocratic pair for a Banach space and also pairs $(\Phi,\Phi)$, where $\Phi$ is an orthonormal system of bounded functions in the spaces $L^{p}$, $p\ne 2$.
Keywords: orthonormal system, democratic and bidemocratic systems, higher rank Haar system, weighted Lebesgue spaces. 
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K. S. Kazarian; A. San Antolin. Wavelets and Bidemocratic Pairs in Weighted Norm Spaces. Matematičeskie zametki, Tome 104 (2018) no. 4, pp. 527-538. http://geodesic.mathdoc.fr/item/MZM_2018_104_4_a3/

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