Geometric Harmonic Analysis IV: Boundary Layer Potentials in Uniformly Rectifiable Domains, and Applications to Complex Analysis

Prefacing the Full Series
Description of Volume IV
Contents
Layer Potential Operators on Lebesgue and Sobolev Spaces
	Comments on History and Physical Interpretations of Harmonic Layer Potentials
	``Tangential\'\' Singular Integral Operators
	A First Look at Layer Potential Operators
	Examples and Alternative Points of View
	Calderón-Zygmund Function Theory for Boundary Layer Potentials
	Cauchy and Cauchy-Clifford Operators on Lebesgue and Sobolev Spaces
	Kernels and Images of Boundary Layer Potentials
	Modified Boundary Layer Potential Operators
Layer Potential Operators on Hardy, BMO, VMO, and Hölder Spaces
	Double Layer Potential Operators on Hardy, BMO, VMO, and Hölder Spaces
	Single Layer Operators Acting from Hardy Spaces
	Integral Operators of Layer Potential Type on Hardy-Based Sobolev Spaces and BMO-1
Layer Potential Operators on Calderón, Morrey-Campanato, and Morrey Spaces
	Boundary Layer Potentials on Calderón Spaces
	Boundary Layer Potentials on Morrey-Campanato Spaces and Their Pre-Duals
	Boundary Layer Potential Operators on Morrey Spaces and Their Pre-Duals
Layer Potential Operators Acting from Boundary Besov and Triebel-Lizorkin Spaces
	Boundary-to-Boundary Layer Potentials from Besov and Triebel-Lizorkin Spaces into Themselves
	Boundary-to-Domain Layer Potentials from Besov Spaces into Weighted Sobolev Spaces
	Boundary-to-Domain Layer Potentials from Besov Spaces into Besov and Triebel-Lizorkin Spaces
	Integral Representation Formulas of Layer Potential Type, and Consequences
Generalized Double Layers in Uniformly Rectifiable Domains
	Theory of Generalized Double Layers
	Generalized Double Layers with Matrix-Valued Kernels, and Chord-Dot-Normal SIO\'s
	Another Look at Standard and Modified Riesz Transforms
Green Formulas and Layer Potential Operators for the Stokes System
	Green-Type Formulas for the Stokes System
	Boundary Layer Potential Operators for the Stokes System: Lebesgue, Sobolev, and Hardy Spaces
	Other Integral Representations and Fatou-Type Results for the Stokes System
	Layer Potentials for the Stokes System on Besov, Triebel-Lizorkin, and Weighted Sobolev Spaces
Applications to Analysis in Several Complex Variables
	CR-Functions and Differential Forms on Boundaries of Locally Finite Perimeter Sets
	Integration by Parts Formulas Involving the  Operator on Sets of Locally Finite Perimeter
	The Bochner-Martinelli Integral Operator
	A Sharp Version of the Bochner-Martinelli-Koppelman Formula and Related Topics
	The Extension Problem for Hölder CR-Functions on Boundaries of Ahlfors Regular Domains
	The Extension Problem for Lp/BMO/VMO/Morrey Functions on Boundaries of Uniformly Rectifiable Domains
	The  Operator and the Dolbeault Complex on Uniformly Rectifiable Sets
Hardy Spaces for Second-Order Weakly Elliptic Operators in the Complex Plane
	Null-Solutions and Boundary Traces for Bitsadze\'s Operator z2 in the Unit Disk
	Null-Solutions and Boundary Traces for the Operator z2-2z2
Terms and notation used in Volume IV
References