Wavelets and Bidemocratic Pairs in Weighted Norm Spaces

摘要

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 (I broken vertical bar, I broken vertical bar), where I broken vertical bar is an orthonormal system of bounded functions in the spaces L-p , p not equal 2.