Zoom 회의실 ID: 814 721 2266
Zoom 회의 참가 https://snu-ac-kr.zoom.us/j/8147212266
The maximal operators associated to averages over geometric objects are important topics in analysis. 
A classical one is the Hardy-Littlewood maximal function.
Averaging and maximal operators associated to more general sets, for example hypersurfaces, have been studied.

In this talk, we study the regularity property of averages over curves and associated maximal bounds.

First of all, we prove the optimal Lp Sobolev regularity estimate for averages over curves in R^d except some endpoint cases.

We settle the conjecture raised by Beltran, Guo, Hickman, and Seeger.

Secondly, we prove the local smoothing estimate of sharp order for averages over curves.

As a consequence, we establish, for the first time, Lp boundedness of the maximal averages over curves when d>3.

Lastly, we prove the maximal bound on the optimal range when d=3.