A weak–type orthogonality principle

Barrionuevo, Jose; Lacey, Michael

doi:10.1090/S0002-9939-02-06744-8

A weak–type orthogonality principle
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by Jose Barrionuevo and Michael T. Lacey PDF

Proc. Amer. Math. Soc. 131 (2003), 1763-1769 Request permission

Abstract:

We prove a weak type estimate for operators of the form $f \to \sum _{s\in \mathbf S}\langle f,\varphi s \rangle \varphi s$ for certain collections of Schwartz functions $\{ \varphi s \}_{s\in \mathbf S}$. This extends some of the orthogonality issues involved in the study of the bilinear Hilbert transform by Lacey and Thiele.

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