<oai_dc:dc xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
<dc:title>Weak type estimates for cone type multipliers associated with a convex polygon</dc:title>
<dc:creator>Sunggeum Hong</dc:creator><dc:creator>Joonil Kim</dc:creator><dc:creator>Chan Yang</dc:creator>
<dc:subject>42B15</dc:subject><dc:subject>42B30</dc:subject><dc:subject>convex polygon</dc:subject><dc:subject>Minkowski functional</dc:subject><dc:subject>cone type multipliers</dc:subject><dc:subject>Hardy spaces</dc:subject>
<dc:description>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 $\rho(\xi) = \inf \{ \varepsilon &gt; 0 : \varepsilon^{-1}\xi \in \mathcal{P} \}$, $\xi \neq 0$. We consider the family of convolution operators $T^{\delta}$ associated with  cone type multipliers \[ \left(1 - \frac{\rho(\xi)^2}{\tau^2} \right)_{+}^{\delta}, \quad (\xi,\tau) \in \mathbb{R}^2 \times \mathbb{R}, \] and show that $T^{\delta}$ is of weak type $(p,p)$ on $H^p(\mathbb{R}^3)$, $\frac{1}{2} &lt; p &lt; 1$ for the critical value $\delta=2(1/p-1)$.</dc:description>
<dc:publisher>Indiana University Mathematics Journal</dc:publisher>
<dc:date>2007</dc:date>
<dc:type>text</dc:type>
<dc:format>pdf</dc:format>
<dc:identifier>10.1512/iumj.2007.56.2946</dc:identifier>
<dc:source>10.1512/iumj.2007.56.2946</dc:source>
<dc:language>en</dc:language>
<dc:relation>Indiana Univ. Math. J. 56 (2007) 1827 - 1869</dc:relation>
<dc:coverage>state-of-the-art mathematics</dc:coverage>
<dc:rights>http://iumj.org/access/</dc:rights>
</oai_dc:dc>