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Wavelets in weighted norm spaces. (English) Zbl 1414.42043

The classes of weight functions for which the higher rank Haar wavelet systems are unconditional bases are investigated. A characterization of such classes of weight functions is presented. It is shown that higher rank Haar wavelets are unconditional bases in the weighted norm Lebesgue spaces. The weights have strong zeros at some points. This shows that the classes of weight functions for which higher rank Haar wavelets are unconditional bases is much richer than it was supposed. The system of Haar functions is one of oldest bases of some functional spaces. The results of the article have scientific interest.

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A25 Rate of convergence, degree of approximation
41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
46B20 Geometry and structure of normed linear spaces
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References:

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