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| Atomic Decompositions of Triebel-Lizorkin Spaces withLocal Weights and Applications? |
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Citation： |
Liguang LIU,Dachun YANG.Atomic Decompositions of Triebel-Lizorkin Spaces withLocal Weights and Applications?[J].Chinese Annals of Mathematics B,2014,35(2):237~260 |
| Page view： 1771
Net amount： 1887 |
Authors： |
Liguang LIU; Dachun YANG; |
Foundation： |
National Natural Science Foundation of China (Nos. 11101425, 11171027)and the Specialized Research Fund for the Doctoral Program of Higher Education of China(No. 20120003110003). |
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| Abstract： |
In this paper, the authors characterize the inhomogeneous Triebel-Lizorkin
spaces Fs,w
p,q (Rn) with local weight w by using the Lusin-area functions for the full ranges
of the indices, and then establish their atomic decompositions for s ∈ R, p ∈ (0, 1] and
q ∈ [p,∞). The novelty is that the weight w here satisfies the classical Muckenhoupt
condition only on balls with their radii in (0, 1]. Finite atomic decompositions for smooth
functions in Fs,w
p,q (Rn) are also obtained, which further implies that a (sub)linear operator
that maps smooth atoms of Fs,w
p,q (Rn) uniformly into a bounded set of a (quasi-)Banach
space is extended to a bounded operator on the whole Fs,w
p,q (Rn). As an application, the
boundedness of the local Riesz operator on the space Fs,w
p,q (Rn) is obtained. |
Keywords： |
Local weight, Triebel-Lizorkin space, Atom, Lusin-Area function, Riesztransform |
Classification： |
46E35, 47B06, 42B20, 42B35 |
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