Distance and Measure in Analysis and Partial Differential Equations

Part I: POINT SPACES * Quasi-Metric Spaces * The Weak Homogeneity Property on Quasi-Metric Spaces * Spaces of Homogeneous Type * Examples * Part II: FUNCTION SPACES * The Hardy--Littlewood Maximal Function and the Differentiation Theorem * Lipschitz Functions * The Space L^2 * Hardy and John--Birenberg Spaces * BMO (f) Spaces * Harnack Inequalities and Hölder--Lipschitz Regularity of Functions * Besov--Taibleson and Triebel--Lizorkin Spaces * Part III: OPERATORS * Weighted Norm Inequalities or the Hardy--Littlewood Maximal Operator * Electrostatic Potentials and Singular Integrals of Calderón--Zygmund Type * Singular Integrals * Unconditional Haar Bases for L^p (1