Weak-Type Bounds for Convolution on the Boolean Hypercube

Junwei Lu, Shengtao Guo, Ethan X. Fang

Let $G$ be the Boolean hypercube which carries uniform measure $\lambda$, and let $T_{\mu }$ denote convolution by a finite positive measure $\mu$ on $G$. For $ψ_μ(u)=\sup\{uλ(\{T_μf\geq u\}):f…