论文标题
加权规范不平等的稳定性
Stability of Weighted Norm Inequalities
论文作者
论文摘要
我们表明，虽然在$ a _ {\ infty} $重量上的bilipschitz变量变化下，单个riesz变换是两个重量标准稳定的，但在变量的旋转变量变量上，它们的重量变量甚至一倍，它们是两个重量标准不稳定。更确切地说，我们表明，在具有完整度量的一组旋转下，各个Riesz变换是不稳定的，其中包括任意接近身份的旋转。这提供了$ a _ {\ infty} $权重和加倍权重之间的操作者理论上的区别。 更普遍地，所有迭代的riesz奇数转换在双倍的重量上旋转不稳定，从而证明了使用测试条件进行双倍措施的迭代riesz变换不平等的特征，而不是典型的“凸起”条件。
We show that while individual Riesz transforms are two weight norm stable under biLipschitz change of variables on $A_{\infty}$ weights, they are two weight norm unstable under even rotational change of variables on doubling weights. More precisely, we show that individual Riesz transforms are unstable under a set of rotations having full measure, which includes rotations arbitrarily close to the identity. This provides an operator theoretic distinction between $A_{\infty}$ weights and doubling weights. More generally, all iterated Riesz transforms of odd order are rotationally unstable on pairs of doubling weights, thus demonstrating the need for characterizations of iterated Riesz transform inequalities using testing conditions for doubling measures, as opposed to the typically stable 'bump' conditions.
