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 |
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 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 252; 2018; 118 ppMSC: 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.
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Table of Contents
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Chapters
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1. Introduction
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2. Preliminaries
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3. Sobolev spaces
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4. Besov spaces
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5. Triebel-Lizorkin spaces
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6. Interpolation
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7. Embedding
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8. Fourier multiplier
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Additional Material
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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