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Sobolev, Besov and Triebel-Lizorkin Spaces on Quantum Tori
 
Xiao Xiong Wuhan University, Wuhan, China and Université de Franche-Comté, Besançon, France
Quanhua Xu Wuhan University, Wuhan, China and Université de Franche-Comté, Besançon, France
Zhi Yin Wuhan University, Wuhan, China
Sobolev, Besov and Triebel-Lizorkin Spaces on Quantum Tori
Softcover ISBN:  978-1-4704-2806-8
Product Code:  MEMO/252/1203
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
eBook ISBN:  978-1-4704-4375-7
Product Code:  MEMO/252/1203.E
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
Softcover ISBN:  978-1-4704-2806-8
eBook: ISBN:  978-1-4704-4375-7
Product Code:  MEMO/252/1203.B
List Price: $156.00 $117.00
MAA Member Price: $140.40 $105.30
AMS Member Price: $93.60 $70.20
Sobolev, Besov and Triebel-Lizorkin Spaces on Quantum Tori
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Sobolev, Besov and Triebel-Lizorkin Spaces on Quantum Tori
Xiao Xiong Wuhan University, Wuhan, China and Université de Franche-Comté, Besançon, France
Quanhua Xu Wuhan University, Wuhan, China and Université de Franche-Comté, Besançon, France
Zhi Yin Wuhan University, Wuhan, China
Softcover ISBN:  978-1-4704-2806-8
Product Code:  MEMO/252/1203
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
eBook ISBN:  978-1-4704-4375-7
Product Code:  MEMO/252/1203.E
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
Softcover ISBN:  978-1-4704-2806-8
eBook ISBN:  978-1-4704-4375-7
Product Code:  MEMO/252/1203.B
List Price: $156.00 $117.00
MAA Member Price: $140.40 $105.30
AMS Member Price: $93.60 $70.20
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2522018; 118 pp
    MSC: Primary 46; Secondary 47; 43

    This paper gives a systematic study of Sobolev, Besov and Triebel-Lizorkin spaces on a noncommutative \(d\)-torus \(\mathbb{T}^d_\theta\) (with \(\theta\) a skew symmetric real \(d\times d\)-matrix). These spaces share many properties with their classical counterparts. The authors prove, among other basic properties, the lifting theorem for all these spaces and a Poincaré type inequality for Sobolev spaces.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Preliminaries
    • 3. Sobolev spaces
    • 4. Besov spaces
    • 5. Triebel-Lizorkin spaces
    • 6. Interpolation
    • 7. Embedding
    • 8. Fourier multiplier
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
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Volume: 2522018; 118 pp
MSC: Primary 46; Secondary 47; 43

This paper gives a systematic study of Sobolev, Besov and Triebel-Lizorkin spaces on a noncommutative \(d\)-torus \(\mathbb{T}^d_\theta\) (with \(\theta\) a skew symmetric real \(d\times d\)-matrix). These spaces share many properties with their classical counterparts. The authors prove, among other basic properties, the lifting theorem for all these spaces and a Poincaré type inequality for Sobolev spaces.

  • Chapters
  • 1. Introduction
  • 2. Preliminaries
  • 3. Sobolev spaces
  • 4. Besov spaces
  • 5. Triebel-Lizorkin spaces
  • 6. Interpolation
  • 7. Embedding
  • 8. Fourier multiplier
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.