论文标题
关于尺寸基准$（1、2、2、1）的单一Brascamp-lieb不平等家庭的家庭
On the family of singular Brascamp-Lieb inequalities with dimension datum $(1, 2, 2, 1)$
论文作者
论文摘要
我们将某些单一的brascamp-lieb表格归类为我们与尺寸基准$（1、2、2、1）$相关联。我们确定了Lebesgue指数的确切范围，为此，该家族内部具有单一的Brascamp Lieb不平等。一个关键的观察结果是一个简单的证明，证明了两个通用和不太通用功能的二元三角式希尔伯特变换中的估计变体。其余的观察结果涉及界定的例子。我们与一个反面示例进行比较，表明三角形的希尔伯特形式不满足指数$（\ infty，p，p，p'）$的奇异brascamp lieb界限。
We classify a certain family of singular Brascamp-Lieb forms which we associate with the dimension datum $(1, 2, 2, 1)$. We determine the exact range of Lebesgue exponents, for which one has singular Brascamp Lieb inequalities within this family. One key observation is a simple proof of a variant of an estimate in dyadic triangular Hilbert transform of two general and one not too general function. The remaining observations concern counter examples to boundedness. We compare with a counter example showing that the triangular Hilbert form does not satisfy singular Brascamp Lieb bounds with exponents $(\infty,p,p')$.
