## Theory of Function Spaces II
The book’s 7 chapters start with a historical survey of the subject, and then analyze the theory of function spaces in Rn and in domains, applications to (exotic) pseudo-differential operators, and function spaces on Riemannian manifolds. ------ Reviews The first chapter deserves special attention. This chapter is both an outstanding historical survey of function spaces treated in the book and a remarkable survey of rather different techniques developed in the last 50 years. It is shown that all these apparently different methods are only different ways of characterizing the same classes of functions. The book can be best recommended to researchers and advanced students working on functional analysis. - Zentralblatt MATH |

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### Contents

Chapter 1 How To Measure Smoothness | 1 |

Definitions and Characterizations | 87 |

Chapter 3 Atoms Oscillations and Distinguished Representations | 159 |

Chapter 4 Key Theorems | 199 |

Chapter 5 Spaces on Domains | 236 |

Chapter 6 Mapping Properties of Pseudodifferential Operators | 255 |

Chapter 7 Spaces on Riemannian Manifoldsand Lie Groups | 280 |

347 | |

367 | |

369 | |