Vol.38 (1) 2016 — 3 articles found.

Résolution du $\partial \bar{\partial}$ pour les courants prolongeables définis sur la boule euclidienne de $C^n$

C. R. Math. Rep. Acad. Sci. Canada Vol. 38 (1) 2016, pp. 36-40
Vol.38 (1) 2016
Salomon Sambou; Eramane Bodian; Dian Diallo Details
(Received: 2014-12-20 , Revised: 2015-05-11 )
(Received: 2014-12-20 , Revised: 2015-05-11 )

Salomon Sambou,Université Assane SECK de Ziguinchor, Sénégal; email: ssambou@univ-zig.sn

Eramane Bodian,Université Assane SECK de Ziguinchor, Sénégal; email: eramane20era@yahoo.fr

Dian Diallo,Université Assane SECK de Ziguinchor, Sénégal; email: diandiallo1086@yahoo.fr

Abstract/Résumé:

We solve the \(\partial \bar{\partial}\)-problem for extendable currents defined on the euclidean ball of \({C}^n\).

On résout le \(\partial \bar{\partial}\) pour les courants prolongeables définis dans la boule euclidienne de \({C}^n\).

Keywords: $\partial \bar{\partial}$, Courant prolongeable, cohomologie de De Rham

AMS Subject Classification: Analytical consequences of geometric convexity (vanishing theorems; etc.) 32F32

PDF(click to download): Résolution du $partial bar{partial}$ pour les courants prolongeables définis sur la boule euclidienne de $C^n$

Sharp Maximal Function Estimates and Boundedness for the Toeplitz Type Operator Associated to a Multiplier Operator

C. R. Math. Rep. Acad. Sci. Canada Vol. 38 (1) 2016, pp. 16-35
Vol.38 (1) 2016
Dazhao Chen Details
(Received: 2014-10-01 , Revised: 2015-04-01 )
(Received: 2014-10-01 , Revised: 2015-04-01 )

Dazhao Chen,Department of Science and Information Science, Shaoyang University, Hunan Shaoyang, 422000, P. R. of China; e-mail: chendazhao27@sina.com

Abstract/Résumé:

In this paper, we establish sharp maximal function estimates for the Toeplitz type operator associated to a certain multiplier operator. As an application, we obtain the boundedness of the operator on Lebesgue, Morrey and Triebel-Lizorkin spaces.

Dans cet article, on établit des estimations de la fonction maximale optimale pour l’opérateur de type Toeplitz associé à un certain opérateur multiplicateur. Comme application, nous obtenons le caractère borné de l’opérateur sur les espaces de Lebesgue, de Morrey et de Triebel-Lizorkin.

Keywords: BMO, Lipschitz function, Morrey space, Toeplitz type operator, Triebel-Lizorkin space, multiplier operator, sharp maximal function

AMS Subject Classification: Singular integrals (Calder__n-Zygmund; etc.), Maximal functions; Littlewood-Paley theory 42B20, 42B25

PDF(click to download): Sharp Maximal Function Estimates and Boundedness for the Toeplitz Type Operator Associated to a Multiplier Operator

Fermionic Realization of Two-Parameter Quantum Affine Algebra $U_{r;s}(C_l^{(1)})$

C. R. Math. Rep. Acad. Sci. Canada Vol. 38 (1) 2016, pp. 1-15
Vol.38 (1) 2016
Naihuan Jing; Honglian Zhang Details
(Received: 2014-11-08 , Revised: 2015-02-27 )
(Received: 2014-11-08 , Revised: 2015-02-27 )

Naihuan Jing,School of Mathematical Sciences, South China University of Technology, Guangzhou 510640,
China and Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA; e-mail: jing@math.ncsu.edu

Honglian Zhang,Department of Mathematics, Shanghai University, Shanghai 200444, China; e-mail: hlzhangmath@shu.edu.cn

Abstract/Résumé:

We construct a Fock space representation and the action of the two-parameter quantum algebra \(U_{r,s}(\frak{gl}_{\infty})\) using extended Young diagrams. In particular, we obtain an integrable representation of the two-parameter quantum affine algebra of type \(C_n^{(1)}\) which is a two-parameter generalization of Kang-Misra-Miwa’s realization.

Nous construisons une représentation sur un espace de Fock de l’algèbre quantique à deux paramètres \(U_{r,s}(\frak{gl}_{\infty})\) en utilisant les diagrammes de Young prolongés. En particulier, on obtient une représentation intégrable de l’algèbre quantique affine à deux paramètres de type \(C_n^{(1)}\) qui est une généralization à deux paramètres de la réalization de Kang-Misra-Miwa.

Keywords: Fock space, Two-parameter quantum ane algebra, Young diagram, fermionic realization

AMS Subject Classification: Quantum groups (quantized enveloping algebras) and related deformations 17B37

PDF(click to download): Fermionic Realization of Two-Parameter Quantum Affine Algebra $U_{r;s}(C_l^{(1)})$