The $H^1(\T^d)$-multiplier norm of Rajchman measures, Zafran-type phenomena, and Walsh--Stieltjes series

Przemysław Ohrysko, Michał Wojciechowski, Bartłomiej Zawalski

We study convolution by complex Rajchman measures as Fourier multipliers on the mean-zero part of the classical isotropic Hardy space $H^1(\T^d)$. Our main technical result gives a…