Szego Seminar: "L^p boundedness of the Riesz transform on R^n"

Abstract: Singular integrals are central to harmonic analysis and are intimately connected with other fields of mathematics such as partial differential equations, operator theory, several complex variables, etc. The Hilbert transform on the real line is a prototype for all singular integrals, and it provides inspirations for subsequent development of the subject. Historically, the theory of singular integrals depended on techniques of complex analysis. However, with the development of Calderon-Zygmund theory, real-variable methods replaced complex analysis. In this talk, we will see an example of using a real-variable method called the method of rotations to extend certain properties, namely the L^p boundedness, of the one-dimensional Hilbert transform to that of its n-dimensional analogue — the Riesz transforms.

Host: Nathan Wagner