Tohoku Mathematical Journal
2018

December
SECOND SERIES VOL. 70, NO. 4

Tohoku Math. J.
70 (2018), 567-605

Title WAVELETS IN WEIGHTED NORM SPACES

Author Kazaros S. Kazarian, Samvel S. Kazaryan and Angel San Antolín

(Received November 24, 2015, revised July 25, 2016)
Abstract. 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.

Mathematics Subject Classification. Primary 41A65; Secondary 41A25, 41A46, 46B20.

Key words and phrases. Wavelet, high rank Haar wavelet, complete orthonormal system, weighted norm space, basis, unconditional basis, weights with singularities.

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