# Weak type estimates for cone type mutipliers associated with convex polygons

Sunggeum Hong
Department of Mathematics, Chosun University
KOREA, REPUBLIC OF

given at  strobl07 (17.06.07)
id:  813
length:  min
status:  accepted
type:  poster
ABSTRACT:
Let $\mathcal{P}$ be a convex polygon in $\mathbb{R}^{2}$
which contains the origin in its interior. Let $\rho$ be the associated
Minkowski functional defined by $\rho(\xi) = \inf \{ \epsilon > 0 : {\epsilon}^{-1}{\xi} \in \mathcal{P}\}, \ \ \xi \neq 0$.
We consider the family of convolution operators ${T}^{\delta}$ associated with
cone type multipliers
\begin{equation*}
{\big (} 1 - \frac{{\rho}({\xi})^2}{\tau^2}
{\big )}_{+}^{\delta}, \ \ \ (\xi,\tau) \in \mathbb{R}^{2} \times
\mathbb{R},
\end{equation*}
and show that ${T}^{\delta}$ is of weak type $(p,p)$ on $H^{p}(\mathbb R^{3})$, $1/2 < p < 1$ for the critical value $\delta = 2(1/p-1)$.

This is a joint work of Sunggeum Hong, Joonil Kim and Chan Woo Yang.

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