Contents
Chapter 1. Introduction
Chapter 2. Preliminaries Concerning Manifolds
2.1. Manifolds
2.2. The Sobolev space
W^P(X,
Y)
2.3. Differential forms
2.4. Mollifiers and smoothing operator
2.5. Maximal operators
Chapter 3. Examples
3.1. The longitude projection
3.2. Spherical coordinates
3.3. Winding around the longitude circles
3.4. A mapping of infinite degree
Chapter 4. Some Classes of Functions
4.1. Marcinkiewicz space «=^eak(^)
4.2. The space
jSfa'*(X)
4.3. The Orlicz space ^f
p
(X)
4.4. Grand
GjSfp-space
4.5. Relations between spaces
4.6. Sobolev classes
Chapter 5. Smooth Approximation
5.1. Web like structures
5.2. Vanishing web oscillations
5.3. Statements of the results
5.4. Proof of Theorem 5.1
5.5. Spinning a web on X
5.6. Proof of Theorems 1.1 and 1.2
5.7. Proof of Theorem 5.2
5.8. Proof of Theorem 1.3
Chapter 6. Jf-^Estimates of the Jacobian
6.1. Weak wedge products
6.2. Distributional Jacobian
6.3. Proof of Theorem 6.5
Chapter 7. Jf^-Estimates
7.1. The Hausdorff content
7.2. The ^ - T h e o r e m
Chapter 8. Degree Theory
1
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