$L^p$-improving bounds of maximal functions along planar curves

Naijia Liu, Haixia Yu

In this paper, we study the $L^p({\mathbb{R}}^2)$-improving bounds, i.e., $L^p({\mathbb{R}}^2)\to L^q({\mathbb{R}}^2)$ estimates, of the maximal function $M_{\gamma }$ along a plane curv…