Boundedness of sublinear operators in Triebel-Lizorkin spaces via atoms

Liguang Liu; Dachun Yang

Liguang Liu ; Dachun Yang

Studia Mathematica, Tome 192 (2009), p. 163-183 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $Ḟ_{p, q}^{s} (ℝ ⁿ)$ to a quasi-Banach space ℬ if and only if sup ${| | T (a) | |}_{ℬ}$ : a is an infinitely differentiable (p,q,s)-atom of $Ḟ_{p, q}^{s} (ℝ ⁿ)$ < ∞, where the (p,q,s)-atom of $Ḟ_{p, q}^{s} (ℝ ⁿ)$ is as defined by Han, Paluszyński and Weiss.

Publié le : 2009-01-01

Zbl 1169.46014

EUDML-ID : urn:eudml:doc:286542

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     title = {Boundedness of sublinear operators in Triebel-Lizorkin spaces via atoms},
     journal = {Studia Mathematica},
     volume = {192},
     year = {2009},
     pages = {163-183},
     zbl = {1169.46014},
     language = {en},
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Liguang Liu; Dachun Yang. Boundedness of sublinear operators in Triebel-Lizorkin spaces via atoms. Studia Mathematica, Tome 192 (2009) pp. 163-183. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm190-2-5/