On the quasi-greedy property and uniformly bounded orthonormal systems
Résumé
We derive a necessary condition for a uniformly bounded orthonormal basis for L2(\Omega), \Omega a probability space, to be quasi-greedy in Lp(\Omega), p \neq 2, and then use this condition to prove that many classical systems, such as the trigonometric system and Walsh system, fail to be quasi-greedy in Lp, p \neq 2, i.e., thresholding is not well-behaved in Lp, p \neq 2, for such systems.
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