The Hilbert transform along vector fields

17 February 2014
Christoph Thiele
An old conjecture by A. Zygmund proposes a Lebesgue Differentiation theorem along a Lipschitz vector field in the plane. E. Stein formulated a corresponding conjecture about the Hilbert transform along the vector field. If the vector field is constant along vertical lines, the Hilbert transform along the vector field is closely related to Carleson's operator. We discuss some progress in the area by and with Michael Bateman and by my student Shaoming Guo.
  • Partial Differential Equations Seminar