Geodesic
An Analog of Titchmarsh's Theorem for the Fourier--Walsh Transform
Matematičeskie zametki, Tome 103 (2018) no. 1, pp. 101-110.

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Using the Fourier–Walsh transform on ${\mathbb R}_+=[0,+\infty)$, we prove a dyadic analog of the classical Titchmarsh theorem on the description of the image under the Fourier transformation of the set of functions satisfying the Lipschitz condition in $L^2$.
Keywords: Fourier–Walsh transform, Lipschitz conditions, dyadic harmonic analysis. 
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S. S. Platonov. An Analog of Titchmarsh's Theorem for the Fourier--Walsh Transform. Matematičeskie zametki, Tome 103 (2018) no. 1, pp. 101-110. http://geodesic.mathdoc.fr/item/MZM_2018_103_1_a8/

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