Cylinder Multipliers Associated with a Convex Polygon

Abstract.

In this paper we prove that sharp weak-type estimates for the maximal operators associated with a cylindric distance function associated with a convex polygon on $H^p({\mathbb{R}}^3)$ when 2/3 < p < 1 and $\delta = 3(\frac{1}{p} - 1)$, or when p = 2/3 and $\delta > 3(\frac{1}{p} - 1)$.