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Mat. Zametki, 2018, Volume 104, Issue 4, Pages 527–538 (Mi mz12148)  

Wavelets and Bidemocratic Pairs in Weighted Norm Spaces

K. S. Kazariana, A. San Antolinb

a Universidad Autonoma de Madrid
b University of Alicante

Abstract: 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.

DOI: https://doi.org/10.4213/mzm12148

Full text: PDF file (511 kB)
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English version:
Mathematical Notes, 2018, 104:4, 508–517

Bibliographic databases:

UDC: 517.5
Received: 17.10.2017

Citation: K. S. Kazarian, A. San Antolin, “Wavelets and Bidemocratic Pairs in Weighted Norm Spaces”, Mat. Zametki, 104:4 (2018), 527–538; Math. Notes, 104:4 (2018), 508–517

Citation in format AMSBIB
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\paper Wavelets and Bidemocratic Pairs in Weighted Norm Spaces
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