## InequalitiesThis classic of the mathematical literature forms a comprehensive study of the inequalities used throughout mathematics. First published in 1934, it presents clearly and lucidly both the statement and proof of all the standard inequalities of analysis. The authors were well-known for their powers of exposition and made this subject accessible to a wide audience of mathematicians. |

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### Contents

INTRODUCTION | 1 |

ELEMENTARY MEAN VALUES | 12 |

MEAN VALUES WITH AN ARBITRARY | 65 |

107110 | 111 |

INTEGRALS | 126 |

SOME APPLICATIONS OF | 172 |

SOME THEOREMS CONCERNING | 196 |

HILBERTS INEQUALITY AND | 227 |

On Hilberts inequality | 308 |

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### Common terms and phrases

analogue applications argument arranged asserts assume belongs best possible bounded chapter coefficients comparable complete concerning condition consider constant continuous convenient convergent convex convex function corresponding curve decreasing deduce defined definition denote depends derived effectively equality equation equivalent example exists extended extremal finite follows further generalisations given gives Hardy Hence Hölder's homogeneous identity important increasing independent inequality infinite integral interesting interval involved less lies limit Littlewood maximum means measure method monotonic necessary and sufficient negative non-negative null observe obtain particular positive proof of Theorem properties proportional prove reduces remarks replace respect result Riesz satisfied sense side similarly simple strictly Suppose symmetrically tends Theorem 13 theory true unless usually values vanish variables variation weights write zero