## Abstract

In this paper the classical Besov spaces B _{p,q} ^{s} and Triebel-Lizorkin spaces F _{p,q} ^{s} for s are generalized in an isotropy way with the smoothness weights {|2j|-ln α}∞-j = 0. These generalized Besov spaces and Triebel-Lizorkin spaces, denoted by B-p,q α and F-p,q α for α^{k} and k , respectively, keep many interesting properties, such as embedding theorems (with scales property for all smoothness weights), lifting properties for all parameters \vec α, and duality for index 0 < p < ∞. By constructing an example, it is shown that there are infinitely many generalized Besov spaces and generalized Triebel-Lizorkin spaces lying between B _{p,q/s} and _{t>s} B _{p,q} ^{t} , and between F _{p,q} ^{s} and _{t>s} F _{p,q} ^{t} , respectively.

Original language | English |
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Pages (from-to) | 336-350 |

Number of pages | 15 |

Journal | Analysis in Theory and Applications |

Volume | 24 |

Issue number | 4 |

DOIs | |

State | Published - Dec 2008 |

## Keywords

- Besov space
- Embedding theorem
- Function space of generalized smoothness
- Triebell-Lizorkin space