The methods covered in the book also attempt to explain different mathematical analyses such as elliptical equations, domination conditions, weighted boundary behavior.
The book serves as a reference work for scholars interested in potential theory and complex analysis.
Table of Contents
Chapter 1 Quasinearly Subharmonic Functions
1.1. Subharmonic Functions and Nearly Subharmonic Functions
1.2. Quasinearly Subharmonic Functions
1.3. Basic Properties of Quasinearly Subharmonic Functions
1.4. Quasinearly Subharmonic Functions and Quasihyperbolic Metric
Chapter 2 Modifications of the Mean Value Inequality For Quasinearly Subharmonic Functions
2.1. Definitions and Related Results
2.2. Generalized Mean Value Inequalities
Chapter 3 a Mean Value Type Inequality for Quasinearly Subharmonic Functions
3.1. Older Mean Value Type Inequalities for Subharmonic Functions
3.2. A Mean Value Type Inequality for Quasinearly Subharmonic Functions
3.2.1. Preliminary Lemmas
3.2.2. A Mean Value Type Inequality for Quasinearly Subharmonic Functions
Chapter 4 Domination Conditions for Families of Quasinearly Subharmonic Functions
4.1. Previous Results
4.2. an Improvement to the Results of Domar and Rippon
Chapter 5 on the Subharmonicity of Separately Subharmonic Functions and Generalizations
5.1. Subharmonic Functions Versus Separately Subharmonic Functions
5.2. Sufficient Conditions for a Separately Subharmonic Function to be Subharmonic
5.2.1. Armitage's and Gardiner's Result
5.2.2. A Further Improvement
5.3. Improvements to the Basic Concise Results Of Lelong, Avanissian, Arsove and Ours
5.3.1. Motivation
5.3.2. A Concise Result for Separately Quasinearly Subharmonic Functions
5.3.3. A Concise Result for Separately Subharmonic Functions
Chapter 6 Separately Subharmonic and Harmonic Functions
6.1. Previous Results
6.2. Arsove's Result
6.3. Improvements to Arsove's Result and to Cegrell's And Sadullaev's Result
6.4. an Improvement to the Result of Koł Odziej And Thorbiörnson
Chapter 7 Weighted Boundary Behavior of Quasinearly S U Bharmonic Functions
7.1. Admissible Functions and Approach Regions
7.2. Previous Weighted Boundary Behavior Results Of Gehring, Hallenbeck, Stoll, Mizuta and Ours
7.3. an Application: on the Radial Order of a Subharmonic Function
7.4. A Limiting Case Result of a Nonintegrability Result Of Suzuki
7.4.1. Suzuki's Result
7.4.2. Our Improvement
Chapter 8 Minkowski Content and Removable Sets For Subharmonic Functions
8.1. Previous Results
8.2. Net Measure and Minkowski Content
8.3. The Results
Chapter 9 Hausdorff Measure and Extension Results For Subharmonic Functions, for Separately Subharmonic Functions, for Harmonic Functions and for Separately Harmonic Functions
9.1. A Result of Federer
9.2. A Result of Blanchet
9.3. an Improvement to the Subharmonic Extension Result Of Blanchet
9.4. an Extension Result for Separately Subharmonic Functions
9.5. an Extension Result for Harmonic Functions
9.6. an Extension Result for Separately Harmonic Functions
Chapter 10 Extension Results for Plurisubharmonic and For Convex Functions
10.1. Previous Results
10.2. Improvements
10.3. The Case of Plurisubharmonic Functions
10.4. The Case of Convex Functions
Chapter 11 Extension Results for Holomorphic and For Meromorphic Functions
11.1. Extension Results for Holomorphic Functions With The Aid of Theorem 9.4
11.2. Exceptional Sets
11.3. A Previous, Slightly Related Result
11.4. Additional Extension Results for Holomorphic and For Meromorphic Functions
11.5. Removable Singularities of Holomorphic Functions With Locally Finite Riesz Mass
Chapter 12 Quasinearly Subharmonic Functions in Locally
12.1. Locally Uniformly Homogeneous Spaces
12.2. Quasinearly Subharmonic Functions
12.3. Examples
12.4. Weighted Boundary Behavior
12.5. Admissible Functions
12.6. Approach Sets
12.7. Ahlfors-Regular Sets
12.8. Boundary Integral Inequalities
- Notation
- References
- Subject Index
Author
- Juhani Riihentaus
