L^p Estimates for a Singular Integral Operator motivated by Calderón's Second Commutator
- Series
- Analysis Seminar
- Time
- Wednesday, December 8, 2010 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Eyvindur Ari Palsson – Cornell University
When Calderón studied his commutators, in connection with the Cauchy
integral on Lipschitz curves, he ran into the bilinear Hilbert
transform by dropping an average in his first commutator. He posed the
question whether this new operator satisfied any L^p estimates. Lacey
and Thiele showed a wide range of L^p estimates in two papers from 1997
and 1999. By dropping two averages in the second Calderón commutator
one bumps into the trilinear Hilbert transform. Finding L^p estimates
for this operator is still an open question.
In my talk I will discuss L^p estimates for a singular integral
operator motivated by Calderón's second commutator by dropping one
average instead of two. I will motivate this operator from a historical
perspective and give some comments on potential applications to partial
differential equations motivated by recent results on the water wave
problem.