Boundedness of sublinear operators in Triebel-Lizorkin spaces via atoms

• Autorzy: Liguang Liu , Dachun Yang
• Języki publikacji: EN

Abstrakty

EN

Let s ∈ ℝ, p ∈ (0,1] and q ∈ [p,∞). It is proved that a sublinear operator T uniquely extends to a bounded sublinear operator from the Triebel-Lizorkin space $Ḟ^{s}_{p,q}(ℝⁿ)$ to a quasi-Banach space ℬ if and only if
sup{$||T(a)||_{ℬ}$: a is an infinitely differentiable (p,q,s)-atom of $Ḟ_{p,q}^{s}(ℝⁿ)$} < ∞,
where the (p,q,s)-atom of $Ḟ_{p,q}^{s}(ℝⁿ)$ is as defined by Han, Paluszyński and Weiss.

Kategorie tematyczne

• 47A30: Norms (inequalities, more than one norm, etc.)
• 42B25: Maximal functions, Littlewood-Paley theory
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 190
• Numer: 2
• Strony: 163-183

Daty

wydano

2009

Twórcy

autor

Liguang Liu

• School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People's Republic of China

autor

Dachun Yang

• School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People's Republic of China

Identyfikatory

DOI

10.4064/sm190-2-5