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

March 31, 2016

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

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