BCAM Working Seminar APDE: Sharp estimates in certain theorems of Marcinkiewicz, Sj-gren and Sj-lin

Abstract
Extending earlier work of Littlewood-Paley and Marcinkiewicz, Sj-gren and Sj-lin showed in 1981 that Littlewood-Paley operators formed with respect to lacunary sets of finite order are $L^p$-bounded for all $1 
Recently, Lerner established sharp weighted $A_2$-estimates for classical Littlewood-Paley operators formed with respect to lacunary sequences, i.e. lacunary sets of order $N=1$. The main aim of this talk is to show how one can use and suitably adapt Lerner´s arguments to obtain sharp weighted $A_2$-estimates for Littlewood-Paley operators formed with respect to lacunary sets of any finite order.

If time permits, some related problems will also be discussed.


Link to the session: https://zoom.us/j/91563668288?pwd=c0E3dklhUHVUeEUzak5LVVZIUFZ5Zz09