The Cauchy Integral in several complex variables

Friday, June 1, 2012 - 11:00am - 12:00pm
Keller 3-180
Loredana Lanzani (University of Arkansas)
The classical Cauchy integral is a fundamental object of complex analysis whose
analytic properties are intimately related to the geometric properties of its supporting curve.

In this talk I will begin by reviewing the most relevant features of the classical Cauchy integral.
I will then move on to the (surprisingly more involved) construction of the Cauchy integral for
a hypersurface in Euclidean complex space.

I will conclude by presenting new results joint with E. M. Stein
concerning the regularity properties of this integral and their relations with the geometry of the hypersurface.

(Time permitting) I will discuss applications of these results to the Szeg\H o and Bergman projections (that is, the orthogonal projections of the Lebesgue space L^2 onto, respectively, the Hardy and Bergman spaces of holomorphic functions).
MSC Code: