Generalized Besov spaces and Triebel-Lizorkin spaces

Huikun Jiang, Chin Cheng Lin

Research output: Contribution to journalArticlepeer-review


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 αk 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 languageEnglish
Pages (from-to)336-350
Number of pages15
JournalAnalysis in Theory and Applications
Issue number4
StatePublished - Dec 2008


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


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