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In this paper, we revisit the square function estimates for extensionoperators over curves with torsion and prove results for planar curves of theform $(T,\phi(T))$ where $\phi(T)$ is a polynomial of degree at least 2. Thisincludes new results for degenerate, finite type curves endowed with theEuclidean 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 characteristic0.

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