Triebel-Lizorkin spaces with non-doubling measures

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

Abstrakty

EN

Suppose that μ is a Radon measure on $ℝ^{d}$, which may be non-doubling. The only condition assumed on μ is a growth condition, namely, there is a constant C₀ > 0 such that for all x ∈ supp(μ) and r > 0,
μ(B(x,r)) ≤ C₀rⁿ,
where 0 < n ≤ d. The authors provide a theory of Triebel-Lizorkin spaces $Ḟ^{s}_{pq}(μ)$ for 1 < p < ∞, 1 ≤ q ≤ ∞ and |s| < θ, where θ > 0 is a real number which depends on the non-doubling measure μ, C₀, n and d. The method does not use the vector-valued maximal function inequality of Fefferman and Stein and is new even for the classical case. As applications, the lifting properties of these spaces by using the Riesz potential operators and the dual spaces are given.

Kategorie tematyczne

• 42B35: Function spaces arising in harmonic analysis
• 46B10: Duality and reflexivity
• 42B25: Maximal functions, Littlewood-Paley theory
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 47B06: Riesz operators; eigenvalue distributions; approximation numbers, s -numbers, Kolmogorov numbers, entropy numbers, etc. of operators
• 43A99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 162
• Numer: 2
• Strony: 105-140

Daty

wydano

2004

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/sm162-2-2