Distance and Measure in Analysis and Partial Differential Equations

Inhaltsverzeichnis zu „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