# Almost Everywhere Convergence of Walsh Series of $L^2$ functions

I am currently reading the Hunt's papar (http://www.mathunion.org/ICM/ICM1970.2/Main/icm1970.2.0655.0662.ocr.pdf), and am wondering if there is any notes which presents his argument more comprehensively.

Thank you.

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## 1 Answer

There are many accounts of this:

1. Thiele's transactions article "The quartile operator and pointwise convergence of Walsh series."
2. Thiele's Book Wave Packet analysis.
3. Tao's wave packet course notes
4. Demeter's recent article "A guide to Carleson's Theorem"
5. This article of Gosselin ("On the convergence of Walsh-Fourier series for $L^2(0,1)$).
6. Billard's original article (in French) "Sur la convergence presque partout des séries de Fourier-Walsh des fonctions de l'espace $L^2(0,1)$"

While Hunt and Billard's arguments are closer to Carleson's original approach to the subject, the first four sources above are closer to the Lacey-Thiele-type arguments. The article of Gosselin follows Fefferman's approach.

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