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math.AP2022
Dimensional estimates for measures on quaternionic spheres
Rami Ayoush, Michał Wojciechowski
In this article we provide lower bounds for the lower Hausdorff dimension of finite measures assuming certain restrictions on their quaternionic spherical harmonics expansion. This…
math.FA2022
On Bernstein type quantitative estimates for Ornstein non-inequalities
Krystian Kazaniecki, Michał Wojciechowski
For the sequence of multi-indexes and we study the inequality \[ \|D^β f\|_{L_1(\mathbb{T}^d)}\leq K_N \sum_{j= 1}^{m} \|D^{α_j}f\|_{L_1(\mathbb{T}^d)}, \]…
math.FA2022
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…