Abstract

Weak-type $(1,1)$ bounds are classically proved with the Calderón–Zygmund decomposition. This gives the right estimates, but rarely good constants, and the constants it gives often grow exponentially with the dimension. In this talk I present two "partial balayage" principles inspired by recent work of Spector and Stockdale: one for linear operators and one for maximal operators. I then apply them to obtain explicit, and in some cases sharp, weak-type constants for the Riesz transforms, the Beurling–Ahlfors transform, the Leray projection, the centered Hardy–Littlewood maximal operator, and the Poisson and heat maximal operators.

Zoom Link

https://us02web.zoom.us/j/87303952902

Organizer

Daniel Spector (NTNU)