Boundedness of sublinear operators in Triebel-Lizorkin spaces via atoms

Liguang Liu, and Dachun Yang. "Boundedness of sublinear operators in Triebel-Lizorkin spaces via atoms." Studia Mathematica 190.2 (2009): 163-183. <http://eudml.org/doc/286542>.

@article{LiguangLiu2009,
abstract = {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.},
author = {Liguang Liu, Dachun Yang},
journal = {Studia Mathematica},
keywords = {Triebel-Lizorkin space; Lusin area function; atom; sublinear operator; quasi-Banach space},
language = {eng},
number = {2},
pages = {163-183},
title = {Boundedness of sublinear operators in Triebel-Lizorkin spaces via atoms},
url = {http://eudml.org/doc/286542},
volume = {190},
year = {2009},
}

TY - JOUR
AU - Liguang Liu
AU - Dachun Yang
TI - Boundedness of sublinear operators in Triebel-Lizorkin spaces via atoms
JO - Studia Mathematica
PY - 2009
VL - 190
IS - 2
SP - 163
EP - 183
AB - 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.
LA - eng
KW - Triebel-Lizorkin space; Lusin area function; atom; sublinear operator; quasi-Banach space
UR - http://eudml.org/doc/286542
ER -