Almost-orthogonality of restricted haar functions

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We consider the Haar functions hI on dyadic intervals. We show that if p > 2 3 and E ⊂ [0, 1], then the set of all functions ∥hI1E∥-1 2 hI1E with |I ∩ E| ≥ p|I| is a Riesz sequence. For p ≤ 2 3 we provide a counterexample.

Original languageEnglish
Pages (from-to)601-609
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number2
Publication statusPublished - Feb 2020
MoE publication typeA1 Journal article-refereed


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