Product Hardy Operators on Hardy Spaces
Product Hardy Operators on Hardy Spaces
We study the product Hausdorff operator $H_{\Phi}$ on the product Hardy spaces, and prove that, for a nonnegative valued function $\Phi$, $H_{\Phi}$ is bounded on the product Hardy space $H^{1}(\mathbb{R}\times \mathbb{R})$ if and only if $\Phi$ is a Lebesgue integrable function on $(0,\infty)\times (0,\infty)$. As an application, we know that …