Cauchy integrals on Lipschitz surfaces in octonionic space

Two Elementary Proofs of the L 2 Boundedness of Cauchy Integrals on Lipschitz Curves

Of the L 2 Boundedness of Cauchy Integrals on Lipschitz Curves

Some remarks about Cauchy integrals

A basic theme in the wonderful books and surveys of Stein, Weiss, and Zygmund is that Hilbert transforms, Poisson kernels, heat kernels, and related objects are quite interesting and fundamental. I certainly like this point of view. There is a variety of ways in which things can be interesting or fundamental, of course. In the last several years there have been striking developments connected t...

Uniqueness Theorems for Cauchy Integrals

If μ is a finite complex measure in the complex plane C we denote by C its Cauchy integral defined in the sense of principal value. The measure μ is called reflectionless if it is continuous (has no atoms) and C = 0 at μ-almost every point. We show that if μ is reflectionless and its Cauchy maximal function Cμ ∗ is summable with respect to |μ| then μ is trivial. An example of a reflectionless m...

On Cauchy Surfaces in Conformally Stationary Spacetimes

A criterion for a spacelike hypersurface in a conformally stationary spacetime to be a Cauchy hypersurface is given. The criterion is based on the forward and the backward completeness of a non-reversible Finsler metric associated to the hypersurface.