论文标题
剪切转换和利兹金空间
The Shearlet Transform and Lizorkin Spaces
论文作者
论文摘要
当限制在所有消失的力矩的情况下，剪切将变换的连续性结果。我们定义了双剪切转换，在此称为剪切合成操作员，我们证明了它在平滑空间上的连续性，并且在$ \ mathbb {r}^2 \ times \ times \ mathbb {r} \ times \ times \ times \ mathbb {r}^r}^\ r}^\ times $上。然后，我们使用这些连续性结果将剪切转换扩展到Lizorkin分布的空间，并证明了它与测试功能的经典定义一致性。
We prove a continuity result for the shearlet transform when restricted to the space of smooth and rapidly decreasing functions with all vanishing moments. We define the dual shearlet transform, called here the shearlet synthesis operator, and we prove its continuity on the space of smooth and rapidly decreasing functions over $\mathbb{R}^2\times\mathbb{R}\times\mathbb{R}^\times$. Then, we use these continuity results to extend the shearlet transform to the space of Lizorkin distributions, and we prove its consistency with the classical definition for test functions.
