Reflectionless measures for Calderón-Zygmund operators I: general theory

We study the properties of reflectionless measures for an s-dimensional Calderón-Zygmund operator T acting in Rd, where s ∈ (0, d). Roughly speaking, these are measures μ for which Tμ(1) is constant on the support of the measure. In this series of papers, we develop the basic theory of reflectionless measures, and describe the relationship between the description of reflectionless measures and certain well-known problems in harmonic analysis and geometric measure theory.