1. Preliminary Information about Integration Theory.- §1. Notation and Terminology.- §2. Some Auxiliary Information about Sets and Functions in Rn.- §3. General Information about Measures and Integrals.- §4. Differentiation Theorems for Measures in Rn.- §5. Generalized Functions.- 2. Functions with Generalized Derivatives.- §1. Sobolev-Type Integral Representations.- §2. Other Integral Representations.- §3. Estimates for Potential-Type Integrals.- §4. Classes of Functions with Generalized Derivatives.- §5. Theorem on the Differentiability Almost Everywhere.- 3. Nonlinear Capacity.- §1. Capacity Induced by a Linear Positive Operator.- §2. The Classes W(T, p, V).- §3. Sets Measurable with Respect to Capacity.- §4. Variational Capacity.- §5. Capacity in Sobolev Spaces.- §6. Estimates of [l, p]-Capacity for Some Pairs of Sets.- §7. Capacity in Besov-Nickolsky Spaces.- 4. Density of Extremal Functions in Sobolev Spaces with First Generalized Derivatives.- §1. Extremal Functions for (l, p)-Capacity.- §2. Theorem on the Approximation of Functions from Lpl by Extremal Functions.- §3. Removable Singularities for the Spaces Lpl (G).- 5. Change of Variables.- §1. Multiplicity of Mapping, Degree of Mapping, and Their Analogies.- §2. The Change of Variable in the Integral for Mappings of Sobolev Spaces.- §3. Sufficient Conditions of Monotonicity and Continuity for the Approximation Functions of the Class Lnl.- §4. Invariance of the Spaces Lpl(G)(Lnl(G)) for Quasiisometric (Quasiconformal) Homeomorphisms.- 6. Extension of Differentiate Functions.- §1. Arc Diameter Condition.- §2. Necessary Extension Conditions for Seminormed Spaces.- §3. Necessary Extension Conditions for Sobolev Spaces.- §4. Necessary Extension Conditions for Besov and Nickolsky Spaces.-§5. Sufficient Extension Conditions.- Comments.- References.
1. Preliminary Information about Integration Theory.- §1. Notation and Terminology.- §2. Some Auxiliary Information about Sets and Functions in Rn.- §3. General Information about Measures and Integrals.- §4. Differentiation Theorems for Measures in Rn.- §5. Generalized Functions.- 2. Functions with Generalized Derivatives.- §1. Sobolev-Type Integral Representations.- §2. Other Integral Representations.- §3. Estimates for Potential-Type Integrals.- §4. Classes of Functions with Generalized Derivatives.- §5. Theorem on the Differentiability Almost Everywhere.- 3. Nonlinear Capacity.- §1. Capacity Induced by a Linear Positive Operator.- §2. The Classes W(T, p, V).- §3. Sets Measurable with Respect to Capacity.- §4. Variational Capacity.- §5. Capacity in Sobolev Spaces.- §6. Estimates of [l, p]-Capacity for Some Pairs of Sets.- §7. Capacity in Besov-Nickolsky Spaces.- 4. Density of Extremal Functions in Sobolev Spaces with First Generalized Derivatives.- §1. Extremal Functions for (l, p)-Capacity.- §2. Theorem on the Approximation of Functions from Lpl by Extremal Functions.- §3. Removable Singularities for the Spaces Lpl (G).- 5. Change of Variables.- §1. Multiplicity of Mapping, Degree of Mapping, and Their Analogies.- §2. The Change of Variable in the Integral for Mappings of Sobolev Spaces.- §3. Sufficient Conditions of Monotonicity and Continuity for the Approximation Functions of the Class Lnl.- §4. Invariance of the Spaces Lpl(G)(Lnl(G)) for Quasiisometric (Quasiconformal) Homeomorphisms.- 6. Extension of Differentiate Functions.- §1. Arc Diameter Condition.- §2. Necessary Extension Conditions for Seminormed Spaces.- §3. Necessary Extension Conditions for Sobolev Spaces.- §4. Necessary Extension Conditions for Besov and Nickolsky Spaces.-§5. Sufficient Extension Conditions.- Comments.- References.
Inhaltsverzeichnis
1. Preliminary Information about Integration Theory.- §1. Notation and Terminology.- §2. Some Auxiliary Information about Sets and Functions in Rn.- §3. General Information about Measures and Integrals.- §4. Differentiation Theorems for Measures in Rn.- §5. Generalized Functions.- 2. Functions with Generalized Derivatives.- §1. Sobolev-Type Integral Representations.- §2. Other Integral Representations.- §3. Estimates for Potential-Type Integrals.- §4. Classes of Functions with Generalized Derivatives.- §5. Theorem on the Differentiability Almost Everywhere.- 3. Nonlinear Capacity.- §1. Capacity Induced by a Linear Positive Operator.- §2. The Classes W(T, p, V).- §3. Sets Measurable with Respect to Capacity.- §4. Variational Capacity.- §5. Capacity in Sobolev Spaces.- §6. Estimates of [l, p]-Capacity for Some Pairs of Sets.- §7. Capacity in Besov-Nickolsky Spaces.- 4. Density of Extremal Functions in Sobolev Spaces with First Generalized Derivatives.- §1. Extremal Functions for (l, p)-Capacity.- §2. Theorem on the Approximation of Functions from Lpl by Extremal Functions.- §3. Removable Singularities for the Spaces Lpl (G).- 5. Change of Variables.- §1. Multiplicity of Mapping, Degree of Mapping, and Their Analogies.- §2. The Change of Variable in the Integral for Mappings of Sobolev Spaces.- §3. Sufficient Conditions of Monotonicity and Continuity for the Approximation Functions of the Class Lnl.- §4. Invariance of the Spaces Lpl(G)(Lnl(G)) for Quasiisometric (Quasiconformal) Homeomorphisms.- 6. Extension of Differentiate Functions.- §1. Arc Diameter Condition.- §2. Necessary Extension Conditions for Seminormed Spaces.- §3. Necessary Extension Conditions for Sobolev Spaces.- §4. Necessary Extension Conditions for Besov and Nickolsky Spaces.-§5. Sufficient Extension Conditions.- Comments.- References.
