Contents:

1. Preliminaries

1.1 Preliminaries on Measure and Integration

1.2 Preliminaries from Functional Analysis

1.3 Semigroups

1.4 Interpolation Spaces

2. Singular Integrals

2.1 Singular Integrals of A.P. Calderion and A. Zygmund

2.2 J. Marcinkiewicz's Interpolation Theorem

2.3 Case of Bounded Kernels

2.4 Case of Continuous Kernels

2.5 Hilbert Transform

2.6 Equimeasurable Functions

2.7Hilbert Transform (Continued)

2.8 Case of Odd Kernels

2.9 Riesz Kernels

2.10 Case of Even Kernels

2.11 General Case

2.12 Derivatives of Homogeneous Functions

3. Sobolev Spaces

3.1 Sobolev Spaces

3.2 Interpolation Inequalities (1)

3.3 Interpolation Inequalities (2)

3.4 Interpolation Inequalities (3)

3.5 Sobolev Spaces in General Domains

3.6 Uniformly Regular Open Sets

3.7 Sobolev Spaces in Uniformly Regular Sets

3.8 Embedding Theorems

3.9 Additional Topics

4. Elliptic Boundary Value Problems

4.1 Fundamental Solutions of Elliptic Operations

4.2 Assumptions and Main Result

4.3 Preliminares from the Theory of Ordinary Differentials Equations

4.4 Case of Constant Coefficients

4.5 Poission Kernels

4.6 Preliminaries on Integral Kernels

4.7 Nonhomogeneous Boundary Conditions

4.8 Problems in Uniformly Regular Open Sets

5. Elliptic Boundary Value Problems (Continued)

5.1 Adjoint Boundary Conditions

5.2 Existence of Solutions

5.3 Estimates of the Kernels

5.4 Boundary Value Problems

5.5 Boundary value Problems in Spaces of Continuous

6. Parabolic Evolution Equations

6.1 Equations wih Coefficients Differentiable in t

6.2 Preliminaries (1)

6.3 Classical Solutions

6.4 Prreliminares (2)

6.5 Strict Solutions

6.6 Maximal Regularity

6.7 An Example

6.8 Equations with Coefficients Holder Continuous in t

6.9 Preliminary Lemmas and Remarks

6.10 Representation of Solutions by Fundamental Solution

6.11 Approximate Equations

6.12 Existence of Solutions

6.13 Application

7. Hyperbolic Evolution Equations

7.1 Admissible Subspaces

7.2 Stable Families of Infinitesimal Generators

7.3 Construction of Evolution Operator (1)

7.4 Uniquences of Regular Solutions

7.5 Construction of Evolution Operator (2)

7.6 Existence of Regular Solutions

7.7 Equations in Hilbert Spaces

7.8 Remark on Applications

8. Retarded Functional Differential Equations

8.1 Maximal Regularity Result

8.2 Assumptions and Notations

8.3 Solvability and Regularity

8.4 Solution Semigroup

8.5 Mild Solutions

8.6 Regularly Accretive Operations

8.7 Semigroup Approach Revised and Control Problem

8.8 Structural Operator

8.9 Controllability and Observability

8.10 Characterization 

8.11 A Special Case

8.12 Eigenmanifold Decomposition

8.13 Second Structural Operator

8.14 A Special Case (Continued)

8.15 F-Completeness of Generalized Eigenfunctions

8.16 Example and Remarks