Analysis Seminar on "Boundedness and compactness of commutator of Cauchy integrals for domains in C^n with minimal smoothness" by Ji Li (Macquarie University, Australia)

Event Type: 
Seminar
Speaker: 
Ji Li (Macquarie University, Sydney, Australia)
Event Date: 
Tuesday, December 11, 2018 -
3:00pm to 4:00pm
Location: 
SMLC 124
Audience: 
Faculty/StaffStudents

Event Description: 

Title: Boundedness and compactness of commutator of Cauchy integrals for domains in C^n with minimal smoothness

Abstract: It is well-known that the commutator of Riesz transform (Hilbert transform in dimension 1) and a symbol b is bounded on L^2(R^n) if and only if b is in the space  of bounded mean oscillation BMO(R^n) (Coifman--Rochberg--Weiss). Moreover, the commutator is compact on L^2(R^n) if and only if b is in the space of vanishing mean oscillation VMO(R^n) (Uchiyama).

We provide such characterisations of the commutator of Cauchy type integrals for domains in C^n with minimal smoothness (studied by Lanzani--Stein), which are singular integrals with non-smooth kernels (beyond the standard frame of Calder\'on--Zygmund operators). It is worth to point out that our method for compactness is new and can recover the known results for standard Calder\'on--Zygmund operators.

 

The results we provide here are based on recent joint works with Xuan Thinh Duong, Michael Lacey and Brett D. Wick.

 

Event Contact

Contact Name: Maria Cristina Pereyra

Contact Phone: (505) 307-9629

Contact Email: crisp@math.unm.edu