We give a complete characterization of the classes of weight functions for which the higher rank Haar wavelet systems are unconditional bases in weighted norm Lebesgue spaces. Particulary it follows that higher rank Haar wavelets are unconditional bases in the weighted norm spaces with weights which have strong zeros at some points. This shows that the class of weight functions for which higher rank Haar wavelets are unconditional bases is much richer than it was supposed.
"Wavelets in weighted norm spaces." Tohoku Math. J. (2) 70 (4) 567 - 605, 2018. https://doi.org/10.2748/tmj/1546570826