Abstract
A complete characterization of weight functions for which the higher-rank Haar wavelets are greedy bases in weighted Lp spaces is given. The proof uses the new concept of a bidemocratic pair for a Banach space and also pairs (Φ, Φ), where Φ is an orthonormal system of bounded functions in the spaces Lp, p≠2.
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Dedicated to the memory of Professor Nikolai K. Karapetiants, a nice person and an excellent mathematician.
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Kazarian, K.S., SanAntolín, A. Wavelets and Bidemocratic Pairs in Weighted Norm Spaces. Math Notes 104, 508–517 (2018). https://doi.org/10.1134/S0001434618090183
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DOI: https://doi.org/10.1134/S0001434618090183