Wavelets and Bidemocratic Pairs in Weighted Norm Spaces

K. S. Kazarian^a, A. San Antolin<sup>b

a</sup> 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.

UDC: 517.5

Received: 17.10.2017

DOI: 10.4213/mzm12148

 English version: Mathematical Notes, 2018, 104:4, 508–517

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