| Preface | p. V |
| Introduction | p. XI |
| Estimates for analytic functions bounded with respect totheir real part | p. 1 |
| Introduction | p. 1 |
| Different proofs of the real-part theorem | p. 2 |
| Extremal values of the real part of the rotated Schwarz kernel | p. 6 |
| Upper estimate of <$>Re { e^{ialpha} Delta f}<$> by the supremum of <$>Re Delta f<$> | p. 8 |
| Two-sided estimates of <$>Re { e^{ialpha} Delta f}<$> by upper and lower bounds of <$>Re Delta f<$> | p. 11 |
| Inequalities for the modulus, real and imaginary parts | p. 12 |
| Variants and extensions | p. 14 |
| Estimates for analytic functions with respect to the Lp-norm of <$>Re Delta f<$> on the circle | p. 17 |
| Introduction | p. 17 |
| Estimate of <$> Re {e^{i alpha} Delta f} <$> by the Lp-norm of <$>Re Delta f<$> on the circle. General case | p. 19 |
| The cases p = 1 and p = 2 | p. 23 |
| The case p = ∞ | p. 25 |
| Generalization of the Carathéodory and Plemelj inequality | p. 30 |
| Variants and extensions | p. 33 |
| Estimates for analytic functions by the best Lp-approximation of <$>Re f<$> on the circle | p. 37 |
| Introduction | p. 37 |
| Estimate of <$> Re { e^{i alpha} Delta f} <$> by the Lp-norm of <$>Re f<$> - c on the circle. General case | p. 39 |
| The cases p=1 and p = 2 | p. 42 |
| The case p = ∞ | p. 43 |
| Inequalities for the real and imaginary parts | p. 49 |
| Estimate for the oscillation of <$>Re { e^{i alpha} f}<$> and its corollaries | p. 51 |
| Variants and extensions | p. 53 |
| Estimates for directional derivatives of harmonic functions | p. 57 |
| Introduction | p. 57 |
| Interior estimates for derivatives in a domain | p. 58 |
| Estimates for directional derivatives with constant direction | p. 61 |
| Estimates for directional derivatives with varying direction | p. 63 |
| Estimates for derivatives of analytic functions | p. 69 |
| Introduction | p. 69 |
| Estimate for <$> | p. 73 |
| Estimate for <$> | p. 75 |
| The case p = 1 and its corollaries | p. 77 |
| Explicit estimate in the case p = 1 | p. 77 |
| Hadamard's real-part theorem for derivatives | p. 78 |
| Landau type inequality | p. 81 |
| Generalization of the Landau inequality | p. 84 |
| Generalization of the Caratheodory inequality | p. 86 |
| The case p = 2 | p. 87 |
| The case p = ∞ | p. 92 |
| Variants and extensions | p. 94 |
| Bohr's type real part estimates | p. 99 |
| Introduction | p. 99 |
| Estimate for the lq-norm of the Taylor series remainder by <$> Re f _1<$> | p. 101 |
| Other estimates for the lq-norm of the Taylor series remainder | p. 103 |
| Bohr's type theorems | p. 109 |
| Variants and extensions | p. 111 |
| Estimates for the increment of derivatives of analytic functions | p. 115 |
| Introduction | p. 115 |
| Estimate for <$> Delta f^{(n)}(z) <$> by <$> Re { f - cal {P}_m } _p<$>. General case | p. 116 |
| The case p = 1 and its corollaries | p. 118 |
| Explicit estimate in the case p = 1 | p. 118 |
| Hadamard-Borel-Carathéodory type inequality for derivatives | p. 119 |
| Landau type inequalities | p. 121 |
| Carathéodory type inequality | p. 124 |
| The cases p =2 and p = ∞ | p. 125 |
| References | p. 129 |
| Index | p. 135 |
| List of Symbols | p. 139 |
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