BiLipschitz (in)stability of weighted norm inequalities for singular integral operators

Michel Alexis, McMaster University

04/05, 2023 at 11:30am-12:30pm (HH207)

We will introduce singular integral operators, which include the Hilbert transform and the Riesz transforms, and discuss characterizations of their operator boundedness between weighted $L^2$ spaces. In particular, we will discuss under what circumstances their boundedness is stable under a biLipschitz change of variables. We will then go through some examples of measure pairs for which biLipschitz stability fails, one being a basic example involving the Hilbert transform, and the other being a pair of doubling measures for which the Riesz transform $R_1$ in the plane is unstable.