## Abstract

In this chapter we study the class of L_{p} spaces, 1 ≤ p≤∞, which is one of the most important classes of symmetric spaces. We begin with the Hölder and Minkowski inequalities and prove that L_{p} is a symmetric space for all 1 ≤ p ≤ ∞. In the case 1 ≤ p < ∞, we show that L_{p} is separable and describe its dual.

Original language | English |
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Title of host publication | Developments in Mathematics |

Publisher | Springer New York LLC |

Pages | 17-27 |

Number of pages | 11 |

DOIs | |

State | Published - 1 Jan 2016 |

### Publication series

Name | Developments in Mathematics |
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Volume | 45 |

ISSN (Print) | 1389-2177 |

## ASJC Scopus subject areas

- Mathematics (all)

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