Reinforcing a Philosophy. A counting approach to square functions over local fields

Contact: Peter Moree (moree@mpim-bonn.mpg.de)

We revisit the square function estimates for extension operators over curves with torsion and prove results for planar curves of the form $(T,\Phi(T))$ where $\Phi(T)$ is a polynomial of
degree at least 2. This includes new results for degenerate, finite type curves endowed with the Euclidean arclength measure such as those given by monomials $\Phi(T)=T^k$ for $k >2.$ Our results are uniform over all local fields of characteristic 0.