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. 
@article{MZM_2018_104_4_a3,
     author = {K. S. Kazarian and A. San Antolin},
     title = {Wavelets and {Bidemocratic} {Pairs} in {Weighted} {Norm} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {527--538},
     publisher = {mathdoc},
     volume = {104},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_4_a3/}
}
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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/