Geometric harmonic analysis ; 4: Boundary layer potentials in uniformly rectifiable domains and applications to complex analysis This monograph presents a comprehensive self contained and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis of geometric measure theoretic flavor capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers graduate students and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis scattering and partial differential equations. Traditionally the label “Calderón Zygmund theory” has been applied to a distinguished body of works primarily pertaining to the mapping properties of singular integral operators on Lebesgue spaces in various geometric settings. Volume IV amounts to a versatile Calderón Zygmund theory for singular integral operators of layer potential type in open sets with uniformly rectifiable boundaries considered on a diverse range of function spaces. Novel applications to complex analysis in several variables are also explored here.