Alexander M. Stokolos

Probabilistic Construction of Kakeya-Type Sets in $\mathbb{R}^2$ associated to separated sets of directions

2024 · arXiv (Cornell University)

We provide a condition on a set of directions $Ω\subset \mathbb{S}^1$ ensuring that the associated directional maximal operator $M_Ω$ is unbounded on $L^p(\mathbb{R}^2)$ for every $1 \leq p < \infty$. The techniques of proof extend …