$L_x^p\to L_{x,u}^q$ estimates for dilated averages over planar curves

Junfeng Li, Naijia Liu, Zengjian Lou +1

In this paper, we consider the $L_x^p({\mathbb{R}}^2)\to L_{x,u}^q({\mathbb{R}}^2\times [1,2])$ estimate for the operator $T$ along a dilated plane curve $(ut,u\gamma (t))$, where $$…