$\ell^2$ Decoupling in $\mathbb R^2$ for curves with Vanishing Curvature

Abstract

We expand the class of curves $(\varphi_1(t),\varphi_2(t)),\ t\in[0,1]$ for which the $\ell^2$ decoupling conjecture holds for $2\leq p\leq 6$. Our class of curves includes all real-analytic regular curves with isolated points of vanishing curvature and all curves of the form $(t,t^{1+\nu})$ for $\nu\in (0,\infty)$.