Harmonic Analysis on Quantum Tori
Abstract This paper is devoted to the study of harmonic analysis on quantum tori. We consider several summation methods on these tori, including the square Fejér means, square and circular Poisson means, and Bochner-Riesz means. We first establish the maximal inequalities for these means, then obtai...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Chen, Zeqian [verfasserIn] |
|---|
| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 2013 |
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| Übergeordnetes Werk: |
Enthalten in: Communications in mathematical physics - Springer Berlin Heidelberg, 1965, 322(2013), 3 vom: 28. Juni, Seite 755-805 |
|---|---|
| Übergeordnetes Werk: |
volume:322 ; year:2013 ; number:3 ; day:28 ; month:06 ; pages:755-805 |
| Links: |
|---|
| DOI / URN: |
10.1007/s00220-013-1745-7 |
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OLC2038904774 |
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| 520 | |a Abstract This paper is devoted to the study of harmonic analysis on quantum tori. We consider several summation methods on these tori, including the square Fejér means, square and circular Poisson means, and Bochner-Riesz means. We first establish the maximal inequalities for these means, then obtain the corresponding pointwise convergence theorems. In particular, we prove the noncommutative analogue of the classical Stein theorem on Bochner-Riesz means. The second part of the paper deals with Fourier multipliers on quantum tori. We prove that the completely bounded Lp Fourier multipliers on a quantum torus are exactly those on the classical torus of the same dimension. Finally, we present the Littlewood-Paley theory associated with the circular Poisson semigroup on quantum tori. We show that the Hardy spaces in this setting possess the usual properties of Hardy spaces, as one can expect. These include the quantum torus analogue of Fefferman’s $ H_{1} $-BMO duality theorem and interpolation theorems. Our analysis is based on the recent developments of noncommutative martingale/ergodic inequalities and Littlewood-Paley-Stein theory. | ||
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10.1007/s00220-013-1745-7 doi (DE-627)OLC2038904774 (DE-He213)s00220-013-1745-7-p DE-627 ger DE-627 rakwb eng 530 510 VZ Chen, Zeqian verfasserin aut Harmonic Analysis on Quantum Tori 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract This paper is devoted to the study of harmonic analysis on quantum tori. We consider several summation methods on these tori, including the square Fejér means, square and circular Poisson means, and Bochner-Riesz means. We first establish the maximal inequalities for these means, then obtain the corresponding pointwise convergence theorems. In particular, we prove the noncommutative analogue of the classical Stein theorem on Bochner-Riesz means. The second part of the paper deals with Fourier multipliers on quantum tori. We prove that the completely bounded Lp Fourier multipliers on a quantum torus are exactly those on the classical torus of the same dimension. Finally, we present the Littlewood-Paley theory associated with the circular Poisson semigroup on quantum tori. We show that the Hardy spaces in this setting possess the usual properties of Hardy spaces, as one can expect. These include the quantum torus analogue of Fefferman’s $ H_{1} $-BMO duality theorem and interpolation theorems. Our analysis is based on the recent developments of noncommutative martingale/ergodic inequalities and Littlewood-Paley-Stein theory. Hardy Space Weak Type Fourier Multiplier Summation Method Maximal Inequality Xu, Quanhua aut Yin, Zhi aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 322(2013), 3 vom: 28. Juni, Seite 755-805 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:322 year:2013 number:3 day:28 month:06 pages:755-805 https://doi.org/10.1007/s00220-013-1745-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_30 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4318 AR 322 2013 3 28 06 755-805 |
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10.1007/s00220-013-1745-7 doi (DE-627)OLC2038904774 (DE-He213)s00220-013-1745-7-p DE-627 ger DE-627 rakwb eng 530 510 VZ Chen, Zeqian verfasserin aut Harmonic Analysis on Quantum Tori 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract This paper is devoted to the study of harmonic analysis on quantum tori. We consider several summation methods on these tori, including the square Fejér means, square and circular Poisson means, and Bochner-Riesz means. We first establish the maximal inequalities for these means, then obtain the corresponding pointwise convergence theorems. In particular, we prove the noncommutative analogue of the classical Stein theorem on Bochner-Riesz means. The second part of the paper deals with Fourier multipliers on quantum tori. We prove that the completely bounded Lp Fourier multipliers on a quantum torus are exactly those on the classical torus of the same dimension. Finally, we present the Littlewood-Paley theory associated with the circular Poisson semigroup on quantum tori. We show that the Hardy spaces in this setting possess the usual properties of Hardy spaces, as one can expect. These include the quantum torus analogue of Fefferman’s $ H_{1} $-BMO duality theorem and interpolation theorems. Our analysis is based on the recent developments of noncommutative martingale/ergodic inequalities and Littlewood-Paley-Stein theory. Hardy Space Weak Type Fourier Multiplier Summation Method Maximal Inequality Xu, Quanhua aut Yin, Zhi aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 322(2013), 3 vom: 28. Juni, Seite 755-805 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:322 year:2013 number:3 day:28 month:06 pages:755-805 https://doi.org/10.1007/s00220-013-1745-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_30 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4318 AR 322 2013 3 28 06 755-805 |
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10.1007/s00220-013-1745-7 doi (DE-627)OLC2038904774 (DE-He213)s00220-013-1745-7-p DE-627 ger DE-627 rakwb eng 530 510 VZ Chen, Zeqian verfasserin aut Harmonic Analysis on Quantum Tori 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract This paper is devoted to the study of harmonic analysis on quantum tori. We consider several summation methods on these tori, including the square Fejér means, square and circular Poisson means, and Bochner-Riesz means. We first establish the maximal inequalities for these means, then obtain the corresponding pointwise convergence theorems. In particular, we prove the noncommutative analogue of the classical Stein theorem on Bochner-Riesz means. The second part of the paper deals with Fourier multipliers on quantum tori. We prove that the completely bounded Lp Fourier multipliers on a quantum torus are exactly those on the classical torus of the same dimension. Finally, we present the Littlewood-Paley theory associated with the circular Poisson semigroup on quantum tori. We show that the Hardy spaces in this setting possess the usual properties of Hardy spaces, as one can expect. These include the quantum torus analogue of Fefferman’s $ H_{1} $-BMO duality theorem and interpolation theorems. Our analysis is based on the recent developments of noncommutative martingale/ergodic inequalities and Littlewood-Paley-Stein theory. Hardy Space Weak Type Fourier Multiplier Summation Method Maximal Inequality Xu, Quanhua aut Yin, Zhi aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 322(2013), 3 vom: 28. Juni, Seite 755-805 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:322 year:2013 number:3 day:28 month:06 pages:755-805 https://doi.org/10.1007/s00220-013-1745-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_30 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4318 AR 322 2013 3 28 06 755-805 |
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10.1007/s00220-013-1745-7 doi (DE-627)OLC2038904774 (DE-He213)s00220-013-1745-7-p DE-627 ger DE-627 rakwb eng 530 510 VZ Chen, Zeqian verfasserin aut Harmonic Analysis on Quantum Tori 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract This paper is devoted to the study of harmonic analysis on quantum tori. We consider several summation methods on these tori, including the square Fejér means, square and circular Poisson means, and Bochner-Riesz means. We first establish the maximal inequalities for these means, then obtain the corresponding pointwise convergence theorems. In particular, we prove the noncommutative analogue of the classical Stein theorem on Bochner-Riesz means. The second part of the paper deals with Fourier multipliers on quantum tori. We prove that the completely bounded Lp Fourier multipliers on a quantum torus are exactly those on the classical torus of the same dimension. Finally, we present the Littlewood-Paley theory associated with the circular Poisson semigroup on quantum tori. We show that the Hardy spaces in this setting possess the usual properties of Hardy spaces, as one can expect. These include the quantum torus analogue of Fefferman’s $ H_{1} $-BMO duality theorem and interpolation theorems. Our analysis is based on the recent developments of noncommutative martingale/ergodic inequalities and Littlewood-Paley-Stein theory. Hardy Space Weak Type Fourier Multiplier Summation Method Maximal Inequality Xu, Quanhua aut Yin, Zhi aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 322(2013), 3 vom: 28. Juni, Seite 755-805 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:322 year:2013 number:3 day:28 month:06 pages:755-805 https://doi.org/10.1007/s00220-013-1745-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_30 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4318 AR 322 2013 3 28 06 755-805 |
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Chen, Zeqian Xu, Quanhua Yin, Zhi |
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Chen, Zeqian |
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10.1007/s00220-013-1745-7 |
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530 510 |
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harmonic analysis on quantum tori |
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Harmonic Analysis on Quantum Tori |
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Abstract This paper is devoted to the study of harmonic analysis on quantum tori. We consider several summation methods on these tori, including the square Fejér means, square and circular Poisson means, and Bochner-Riesz means. We first establish the maximal inequalities for these means, then obtain the corresponding pointwise convergence theorems. In particular, we prove the noncommutative analogue of the classical Stein theorem on Bochner-Riesz means. The second part of the paper deals with Fourier multipliers on quantum tori. We prove that the completely bounded Lp Fourier multipliers on a quantum torus are exactly those on the classical torus of the same dimension. Finally, we present the Littlewood-Paley theory associated with the circular Poisson semigroup on quantum tori. We show that the Hardy spaces in this setting possess the usual properties of Hardy spaces, as one can expect. These include the quantum torus analogue of Fefferman’s $ H_{1} $-BMO duality theorem and interpolation theorems. Our analysis is based on the recent developments of noncommutative martingale/ergodic inequalities and Littlewood-Paley-Stein theory. © Springer-Verlag Berlin Heidelberg 2013 |
| abstractGer |
Abstract This paper is devoted to the study of harmonic analysis on quantum tori. We consider several summation methods on these tori, including the square Fejér means, square and circular Poisson means, and Bochner-Riesz means. We first establish the maximal inequalities for these means, then obtain the corresponding pointwise convergence theorems. In particular, we prove the noncommutative analogue of the classical Stein theorem on Bochner-Riesz means. The second part of the paper deals with Fourier multipliers on quantum tori. We prove that the completely bounded Lp Fourier multipliers on a quantum torus are exactly those on the classical torus of the same dimension. Finally, we present the Littlewood-Paley theory associated with the circular Poisson semigroup on quantum tori. We show that the Hardy spaces in this setting possess the usual properties of Hardy spaces, as one can expect. These include the quantum torus analogue of Fefferman’s $ H_{1} $-BMO duality theorem and interpolation theorems. Our analysis is based on the recent developments of noncommutative martingale/ergodic inequalities and Littlewood-Paley-Stein theory. © Springer-Verlag Berlin Heidelberg 2013 |
| abstract_unstemmed |
Abstract This paper is devoted to the study of harmonic analysis on quantum tori. We consider several summation methods on these tori, including the square Fejér means, square and circular Poisson means, and Bochner-Riesz means. We first establish the maximal inequalities for these means, then obtain the corresponding pointwise convergence theorems. In particular, we prove the noncommutative analogue of the classical Stein theorem on Bochner-Riesz means. The second part of the paper deals with Fourier multipliers on quantum tori. We prove that the completely bounded Lp Fourier multipliers on a quantum torus are exactly those on the classical torus of the same dimension. Finally, we present the Littlewood-Paley theory associated with the circular Poisson semigroup on quantum tori. We show that the Hardy spaces in this setting possess the usual properties of Hardy spaces, as one can expect. These include the quantum torus analogue of Fefferman’s $ H_{1} $-BMO duality theorem and interpolation theorems. Our analysis is based on the recent developments of noncommutative martingale/ergodic inequalities and Littlewood-Paley-Stein theory. © Springer-Verlag Berlin Heidelberg 2013 |
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Harmonic Analysis on Quantum Tori |
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