论文标题
异国情调的calderón-zygmund操作员
Exotic Calderón-Zygmund operators
论文作者
论文摘要
我们研究了与标准Calderón-Zygmund内核更奇异的核的单数积分运算符，但比双参数产品Calderón-Zygmund内核更单数。这些内核是对某些适合所谓Zygmund扩张的某些三维内核的限制的限制，这是我们研究这些物体的动机的一部分。我们证明，这样的内核可以在许多方面被视为标准内核扩展领域的一部分，因为它们证明它们满足了T1定理和换向器的估计，以一种让人联想到标准Calderón-Zygmund内核的相应结果的形式。但是，我们表明，一般而言，单参数加权估计失败。
We study singular integral operators with kernels that are more singular than standard Calderón-Zygmund kernels, but less singular than bi-parameter product Calderón-Zygmund kernels. These kernels arise as restrictions to two dimensions of certain three-dimensional kernels adapted to so-called Zygmund dilations, which is part of our motivation for studying these objects. We make the case that such kernels can, in many ways, be seen as part of the extended realm of standard kernels by proving that they satisfy both a T1 theorem and commutator estimates in a form reminiscent of the corresponding results for standard Calderón-Zygmund kernels. However, we show that one-parameter weighted estimates, in general, fail.
