Eyvindur Ari Palsson
Eyvindur Ari Palsson

Ph.D. (2011) Cornell University

First Position
Dissertation
Advisor:
Research Area:
Abstract: My research centers on L^{p} estimates for singular integral operators using techniques from real harmonic analysis. In particular I use timefrequency analysis and oscillatory integral theory. Singular integral operators are frequently motivated by, and have potential applications to, nonlinear partial differential equations.
In my thesis I show a wide range of L^{p} estimates for an operator motivated by dropping one average in Calderón's second commutator. For comparison by dropping one average in Calderón's first commutator one faces the bilinear Hilbert transform. Lacey and Thiele showed L^{p} estimates for that operator. By dropping two averages in Calderón's second commutator one obtains the trilinear Hilbert transform. No L^{p} estimates are known for that operator. The novelty in this thesis is that in order to avoid difficulty of the level of the trilinear Hilbert transform, I choose to view the symbol of the operator as a nonstandard symbol.