Abstract
Rychkov defined weighted Besov spaces and weighted Triebel-Lizorkin spaces coming with a weight in the class Ap loc, which is even wider than the class Ap due to Muckenhoupt. In the present paper we are concerned with the atomic decomposition of these spaces. As an application, we obtain some key theorems in the theory of function spaces. Finally we conclude this paper with some helpful examples showing the difference between weighted spaces and unweighted spaces.
| Original language | English |
|---|---|
| Pages (from-to) | 103-126 |
| Number of pages | 24 |
| Journal | Mathematische Nachrichten |
| Volume | 285 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jan 2012 |
| Externally published | Yes |
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Keywords
- Atom
- Besov space
- Decomposition of functions
- Triebel-Lizorkin space
- Weights
ASJC Scopus subject areas
- Mathematics(all)
Cite this
Atomic decomposition for weighted Besov and Triebel-Lizorkin spaces. / Izuki, Mitsuo; Sawano, Yoshihiro.
In: Mathematische Nachrichten, Vol. 285, No. 1, 01.2012, p. 103-126.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Atomic decomposition for weighted Besov and Triebel-Lizorkin spaces
AU - Izuki, Mitsuo
AU - Sawano, Yoshihiro
PY - 2012/1
Y1 - 2012/1
N2 - Rychkov defined weighted Besov spaces and weighted Triebel-Lizorkin spaces coming with a weight in the class Ap loc, which is even wider than the class Ap due to Muckenhoupt. In the present paper we are concerned with the atomic decomposition of these spaces. As an application, we obtain some key theorems in the theory of function spaces. Finally we conclude this paper with some helpful examples showing the difference between weighted spaces and unweighted spaces.
AB - Rychkov defined weighted Besov spaces and weighted Triebel-Lizorkin spaces coming with a weight in the class Ap loc, which is even wider than the class Ap due to Muckenhoupt. In the present paper we are concerned with the atomic decomposition of these spaces. As an application, we obtain some key theorems in the theory of function spaces. Finally we conclude this paper with some helpful examples showing the difference between weighted spaces and unweighted spaces.
KW - Atom
KW - Besov space
KW - Decomposition of functions
KW - Triebel-Lizorkin space
KW - Weights
UR - http://www.scopus.com/inward/record.url?scp=83155192896&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=83155192896&partnerID=8YFLogxK
U2 - 10.1002/mana.200910201
DO - 10.1002/mana.200910201
M3 - Article
VL - 285
SP - 103
EP - 126
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
SN - 0025-584X
IS - 1
ER -