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ix | |
| Preface |
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xiii | |
| Acknowledgements |
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xvii | |
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Definition of the families fα |
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1 | (1) |
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Relations between fα and H1 |
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2 | (2) |
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The Riesz-Herglotz formula |
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4 | (1) |
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Representations with real measures and h1 |
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5 | (2) |
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The F. and M. Riesz theorem |
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7 | (2) |
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The representing measures for functions in fα |
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9 | (2) |
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The one-to-one correspondence between measures and functions in the Riesz-Herglotz formula |
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11 | (1) |
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The Banach space structure of fα |
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11 | (2) |
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Norm convergence and convergence uniform on compact sets |
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13 | (2) |
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15 | (2) |
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Properties of the gamma function and the binomial coefficients |
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17 | (5) |
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22 | (2) |
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Membership of f and f' in fα |
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24 | (2) |
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The inclusion of fα in fβ when 0 ≤ α < β |
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26 | (1) |
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The union of fα for α > 0 |
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26 | (2) |
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28 | (1) |
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An integral condition for membership in fα when α > 1 |
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29 | (1) |
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Besov spaces and their relationship to fα |
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30 | (4) |
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Infinite Blaschke products and membership in fα |
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34 | (4) |
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The inner function S and its membership in fα |
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38 | (3) |
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Hadamard products and relations with f1 and H∞ |
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41 | (5) |
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46 | (1) |
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Integral Means and the Hardy and Dirichlet Spaces |
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47 | (1) |
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48 | (1) |
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Estimates on integral means |
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49 | (3) |
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Relations between fα and Hp |
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52 | (3) |
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Growth of the integral means of f when f ε fα α > and 0 < p > 1 |
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55 | (2) |
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The Dirichlet spaces and fα |
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57 | (3) |
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60 | (1) |
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61 | (3) |
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Membership of inner functions in Dirichlet spaces, Besov spaces and fα |
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64 | (1) |
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65 | (3) |
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Boundary functions and weak Lp inequalities |
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68 | (4) |
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72 | (1) |
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Radial limits and nontangential limits of bounded functions |
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73 | (2) |
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Local integrability conditions and radial limits |
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75 | (3) |
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78 | (3) |
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Nondecreasing functions and α-capacity |
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81 | (3) |
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Nontangential limits and exceptional sets of zero α-capacity |
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84 | (1) |
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Growth and countable exceptional sets |
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85 | (1) |
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Growth and exceptional sets of measure zero |
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86 | (4) |
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90 | (3) |
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The moduli of the zeros of a function in fα when α > 1 |
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93 | (2) |
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95 | (4) |
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Functions with large growth when fα 1 |
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99 | (5) |
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Functions with zeros tending slowly to T |
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104 | (2) |
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106 | (1) |
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Multipliers: Basic Results |
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The multiplication operator and the definition of Mα |
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107 | (3) |
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The Banach space structure of Mα |
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110 | (2) |
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The inclusion of Mα in Mβ when 0 > α < β |
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112 | (1) |
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113 | (2) |
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115 | (1) |
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115 | (6) |
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An assumption on integrability sufficient to imply a Lipschitz condition |
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121 | (6) |
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A sufficient condition for a multiplier when 0 < a < 1 |
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127 | (3) |
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130 | (5) |
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Multipliers: Further Results |
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A lemma about Toeplitz operators and M1 |
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135 | (4) |
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An integralbility condition on the second difference |
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139 | (5) |
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144 | (1) |
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Conditions on the Taylor coefficients |
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145 | (2) |
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147 | (13) |
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160 | (1) |
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161 | (1) |
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162 | (7) |
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The singular inner function S |
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169 | (12) |
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Strict monotonicity of multiplier spaces |
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181 | (1) |
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A survey of facts about M0 |
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181 | (2) |
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183 | (3) |
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Composition with conformal automorphisms |
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186 | (1) |
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Factorization in the case of finitely many zeros |
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187 | (3) |
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Factorization with infinite Blaschke products when α = 1 |
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190 | (2) |
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192 | (1) |
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A product theorem for subordination families |
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192 | (1) |
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The closed convex hull of subordination classes |
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193 | (1) |
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Composition operators when α ≥ 1 |
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194 | (3) |
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Excluded rays and membership in &fα |
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197 | (2) |
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The hereditary property of composition operators for increasing α |
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199 | (1) |
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A Taylor series condition for a composition operator |
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200 | (2) |
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202 | (2) |
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The closed convex hull of starlike and of convex mappings |
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204 | (3) |
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207 | (1) |
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A sufficient condition for membership in f2 |
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207 | (1) |
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Spirallike and close-to-convex mappings |
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208 | (2) |
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Univalent functions which do not belong to f2 |
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210 | (2) |
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The maximum modulus and membership in fα |
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212 | (2) |
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Univalent self-maps of the disk and composition operators |
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214 | (2) |
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216 | (1) |
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A Characterization of Cauchy Transforms |
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The one-to-one mapping between measures and functions |
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217 | (5) |
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Necessary conditions for representation as a Cauchy transform |
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222 | (1) |
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The composition of a subharmonic function and an analytic function |
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223 | (2) |
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The subharmonicity of the special function up |
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225 | (2) |
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A key lemma for representation by a real measure |
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227 | (4) |
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Sufficient conditions for representation as a Cauchy transform |
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231 | (3) |
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234 | (3) |
| References |
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237 | (10) |
| Index |
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247 | |
Lisainfo e-raamatute kohta