Atomic decomposition for weighted Besov and Triebel-Lizorkin spaces

Mitsuo Izuki; Yoshihiro Sawano

doi:10.1002/mana.200910201

Atomic decomposition for weighted Besov and Triebel-Lizorkin spaces

Mitsuo Izuki, Yoshihiro Sawano

Graduate School of Education

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

Rychkov defined weighted Besov spaces and weighted Triebel-Lizorkin spaces coming with a weight in the class A_p^loc, which is even wider than the class A_p 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	https://doi.org/10.1002/mana.200910201
Publication status	Published - Jan 2012

Keywords

Atom
Besov space
Decomposition of functions
Triebel-Lizorkin space
Weights

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1002/mana.200910201

Cite this

@article{ac917609347f48f682a4a3de8362da1a,

title = "Atomic decomposition for weighted Besov and Triebel-Lizorkin spaces",

abstract = "Rychkov defined weighted Besov spaces and weighted Triebel-Lizorkin spaces coming with a weight in the class Aploc, 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.",

keywords = "Atom, Besov space, Decomposition of functions, Triebel-Lizorkin space, Weights",

author = "Mitsuo Izuki and Yoshihiro Sawano",

year = "2012",

month = jan,

doi = "10.1002/mana.200910201",

language = "English",

volume = "285",

pages = "103--126",

journal = "Mathematische Nachrichten",

issn = "0025-584X",

publisher = "Wiley-VCH Verlag",

number = "1",

}

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 Aploc, 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 Aploc, 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

AN - SCOPUS:83155192896

VL - 285

SP - 103

EP - 126

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

SN - 0025-584X

IS - 1

ER -

Atomic decomposition for weighted Besov and Triebel-Lizorkin spaces

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this