Function spaces on quantum tori

Xiao Xiong; Quanhua Xu; Zhi Yin

doi:10.1016/j.crma.2015.06.002

Function spaces on quantum tori

CNRS
Wuhan University

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

6 Scopus citations

Abstract

We study Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori. These spaces share many properties with their classical counterparts. The results announced include: Besov and Sobolev embedding theorems; Littlewood-Paley-type characterizations of Besov and Triebel-Lizorkin spaces; an explicit description of the K-functional of (L_p(T^d_θ), W^k_p(T^d_θ)); descriptions of completely bounded Fourier multipliers on these spaces.

Original language	English
Pages (from-to)	729-734
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	353
Issue number	8
DOIs	https://doi.org/10.1016/j.crma.2015.06.002
State	Published - 2015
Externally published	Yes

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10.1016/j.crma.2015.06.002

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title = "Function spaces on quantum tori",

abstract = "We study Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori. These spaces share many properties with their classical counterparts. The results announced include: Besov and Sobolev embedding theorems; Littlewood-Paley-type characterizations of Besov and Triebel-Lizorkin spaces; an explicit description of the K-functional of (Lp(Tdθ), Wkp(Tdθ)); descriptions of completely bounded Fourier multipliers on these spaces.",

author = "Xiao Xiong and Quanhua Xu and Zhi Yin",

note = "Publisher Copyright: {\textcopyright} 2015 Acad{\'e}mie des sciences.",

year = "2015",

doi = "10.1016/j.crma.2015.06.002",

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volume = "353",

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journal = "Comptes Rendus Mathematique",

issn = "1631-073X",

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T1 - Function spaces on quantum tori

AU - Xiong, Xiao

AU - Xu, Quanhua

AU - Yin, Zhi

PY - 2015

Y1 - 2015

N2 - We study Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori. These spaces share many properties with their classical counterparts. The results announced include: Besov and Sobolev embedding theorems; Littlewood-Paley-type characterizations of Besov and Triebel-Lizorkin spaces; an explicit description of the K-functional of (Lp(Tdθ), Wkp(Tdθ)); descriptions of completely bounded Fourier multipliers on these spaces.

AB - We study Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori. These spaces share many properties with their classical counterparts. The results announced include: Besov and Sobolev embedding theorems; Littlewood-Paley-type characterizations of Besov and Triebel-Lizorkin spaces; an explicit description of the K-functional of (Lp(Tdθ), Wkp(Tdθ)); descriptions of completely bounded Fourier multipliers on these spaces.

UR - https://www.scopus.com/pages/publications/85027926612

U2 - 10.1016/j.crma.2015.06.002

DO - 10.1016/j.crma.2015.06.002

M3 - 文章

AN - SCOPUS:85027926612

SN - 1631-073X

VL - 353

SP - 729

EP - 734

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 8

ER -

Function spaces on quantum tori

Abstract

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