Cover......Page 1
Title......Page 3
Series editor's preface......Page 5
Table of contents......Page 7
Preface......Page 10
1.1. The definitions of n(r, a), N(r, a), b(r,f), q(r,f), m(r,f), m2(r,f) A(r,f),S(r,f) and T(r,f)......Page 11
1.2. Convex function......Page 12
1.3. The properties of A(r, f)......Page 13
1.4. The properties of S(r, f)......Page 15
1.5. The properties of m(r, f'//)......Page 20
1.6. The relationships among T(r,f), T(r,f) and N(r,fi, etc.......Page 26
1.7. The infinite product representations of a meromorphic function......Page 32
2.1. The concept of normal family......Page 36
2.2. The properties of the normal families of meromorphic functions......Page 37
3. The distance of a family of functions at a point......Page 48
4. On meromorphic functions with deficient values......Page 52
5. The applications of the theory of normal families......Page 63
6. Application to univalent functions......Page 70
1.1. Harmonic Functions......Page 78
1.2. Boundary behaviors of Poisson-Stieltjes integrals......Page 81
1.3. Subharmonic functions......Page 83
1.4. The convexity theorem of Hardy......Page 86
1.5. Subordination......Page 88
2.1. Boundary values......Page 89
2.2. Zeros......Page 92
2.3. The meaning of converging to the boundary values......Page 94
2.4. Canonical factorization......Page 98
3.1. Poisson integral and H1......Page 100
3.2. Banach space......Page 102
1.1. Vector-valued bounded variation......Page 104
1.2. Vector-valued integration......Page 105
1.3. Vector-valued Holder condition......Page 110
1.4. Vector-valued regular functions......Page 112
1.5. Compactness and convergence in the space of vector-valued regular functions......Page 117
1.6. Boundary properties of a class of the vector-valued regular functions in S(0, 1)......Page 120
1.7. Vector-valued elliptic functions......Page 123
2.1. Vector-valued Cauchy type integrals......Page 127
2.2. Vector-valued singular integral equations......Page 129
2.3. Vector-valued doubly-periodic Riemann boundary value problems......Page 133
2.4. Vector-valued boundary value problems with the boundary being a straight line......Page 137
2.5. The solutions of the vector-valued disturbance problem......Page 143
2.6. The vector-valued boundary value problems in lp......Page 141
3.1. G-differentiability......Page 155
3.2. Vector-valued regular functions in locally convex spaces......Page 158
Bibliography......Page 161
Index of symbols......Page 164
Index......Page 167
Back cover......Page 171