Title: On the boundedness of non-integer dimension Calderón-Zygmund Operators with anti-symmetric kernels
Abstract: On this poster, we shall describe the ideas behind the result in the preprint arXiv:1604.02014 (joint work with Fedor Nazarov), where the boundedness of all odd anti-symmetric Calderón-Zygmund operators of a fixed non-integer dimension is shown to be equivalent to the boundedness of a certain positive operator involving a Wolff potential. The point is that the latter condition encodes all the cancellation that may occur in the singular integral operators in a positive condition. The argument presented in the preprint serves as an idealized version of the proof from a much more delicate work with Fedja, Maria Carmen Reguera, and Xavier Tolsa (arXiv:1602.02821) concerning the Riesz transform of co-dimension smaller than one.