Multilinear Dyadic Operators and Their Commutators

Dissertation Defense
Tuesday, July 18, 2017 - 16:00
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech
In this thesis, we introduce multilinear dyadic paraproducts and Haar multipliers, and discuss boundedness properties of these operators and their commutators with locally integrable functions in various settings. We also present pointwise domination of these operators by multilinear sparse operators, which we use to prove multilinear Bloom’s inequality for the commutators of multilinear Haar multipliers. Along the way, we provide several characterizations of dyadic BMO functions.