Some new spaces of Besov and Triebel-Lizorkin type on homogeneous spaces

• Autorzy: Yongsheng Han , Dachun Yang
• Języki publikacji: EN

Abstrakty

EN

New norms for some distributions on spaces of homogeneous type which include some fractals are introduced. Using inhomogeneous discrete Calderón reproducing formulae and the Plancherel-Pólya inequalities on spaces of homogeneous type, the authors prove that these norms give a new characterization for the Besov and Triebel-Lizorkin spaces with p, q > 1 and can be used to introduce new inhomogeneous Besov and Triebel-Lizorkin spaces with p, q ≤ 1 on spaces of homogeneous type. Moreover, atomic decompositions of these new spaces are also obtained. All the results of this paper are new even for ℝⁿ.

Kategorie tematyczne

• 42B35: Function spaces arising in harmonic analysis
• 42B25: Maximal functions, Littlewood-Paley theory
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 43A99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 156
• Numer: 1
• Strony: 67-97

Daty

wydano

2003

Twórcy

autor

Yongsheng Han

• Department of Mathematics, Auburn University, Auburn, AL 36849-5310, U.S.A.

autor

Dachun Yang

• Department of Mathematics, Beijing Normal University, Beijing 100875, People's Republic of China

Identyfikatory

DOI

10.4064/sm156-1-5