  In this paper, 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 $k \geq 3$. Our results are uniform over all local fields of characteristic
0.
