Abstract
AbstractWe 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.
Funder
Academy of Finland
University of Helsinki internal grants for the Centre of Excellence in Analysis and Dynamics Research
Finnish Centre of Excellence in Randomness and Structures “FiRST”
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
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