## Theory of Function SpacesThe book deals with the two scales Bsp,q and Fsp,q of spaces of distributions, where ‐∞s∞ and 0p,q≤∞, which include many classical and modern spaces, such as Hölder spaces, Zygmund classes, Sobolev spaces, Besov spaces, Bessel-potential spaces, Hardy spaces and spaces of BMO-type. It is the main aim of this book to give a unified treatment of the corresponding spaces on the Euclidean n-space Rsubn |

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### Contents

2 Function Spaces on Rn | 33 |

3 Function Spaces on Domains | 188 |

4 Regular Elliptic Differential Equations | 212 |

5 Homogeneous Function Spaces | 237 |

6 UltraDistributions and Weighted Spaces of Entire Analytic Functions | 245 |

7 Weighted Function Spaces on Rn | 254 |

8 Weighted Function Spaces on Domains and Degenerate Elliptic Differential Equations | 260 |

9 Periodic Function Spaces | 264 |

10 Further Types of Function Spaces | 269 |

274 | |

284 | |

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### Common terms and phrases

analytic functions arbitrary assertion assume Banach space Besov spaces Bessel-potential spaces Chapter characteristic function classical compact subset compact support complex interpolation consequence continuous embedding coretraction Corollary denoted E. M. Stein equivalent norm equivalent quasi-norm exists a constant exists a positive extended Fourier multiplier theorem FsM(Rn function on Rn function spaces Furthermore given Hardy spaces Hence holds homogeneous spaces Hp(Bn independent infimum infimum is taken infinitely differentiable function integer interpolation formula interpolation method interpolation property Lebesgue measure Lemma Let Q Lp(Bn Lp(Rn mapping maximal functions modification if q multi-index natural number obtain particular Peetre pointwise polynomial positive constant positive number problem proof is complete proof of Theorem Proposition quasi-Banach space real interpolation real number recall regular elliptic system Remark replace respectively restriction right-hand side S. M. Nikol'skij S(Rn Schauder basis Similarly Sobolev spaces Step subsection subset of Rn supp Triebel x£Rn yields