On measures with $L^2$ bounded Riesz transform: to AD regularity and beyond!

Abstract

The measures which define an $L^2$ bounded $n$-dimensional Riesz transform have been intensely studied in the last 50 years. Especially in the case of $n$-AD-regular measures (that is, measures that are quantitatively $n$-dimensional) the situation is very well understood by now. In this talk I will describe how some of the recent advances in the field can be pushed beyond the AD-regular setting. Based on joint work with Xavier Tolsa.

Damian Dąbrowski

Postdoc in mathematics

My research interests include geometric measure theory and harmonic analysis.