Banach Journal of Mathematical Analysis

Sharp maximal function inequalities and boundedness for Toeplitz type operator related to general fractional integral operators

Lanzhe Liu

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Abstract

In this paper, we establish sharp maximal function inequalities for the Toeplitz type operator related to some general fractional integral operators. As an application, we obtain the boundedness of the operator on Lebesgue, Morrey and Triebel-Lizorkin spaces. The operators include Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.

Article information

Source
Banach J. Math. Anal., Volume 7, Number 1 (2013), 142- 159.

Dates
First available in Project Euclid: 22 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1358864555

Digital Object Identifier
doi:10.15352/bjma/1358864555

Mathematical Reviews number (MathSciNet)
MR3004273

Zentralblatt MATH identifier
1277.47044

Subjects
Primary: 47A10: Spectrum, resolvent
Secondary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25: Maximal functions, Littlewood-Paley theory

Keywords
Toeplitz type operator sharp maximal function Morrey space $BMO$ Lipschitz function

Citation

Liu, Lanzhe. Sharp maximal function inequalities and boundedness for Toeplitz type operator related to general fractional integral operators. Banach J. Math. Anal. 7 (2013), no. 1, 142-- 159. doi:10.15352/bjma/1358864555. https://projecteuclid.org/euclid.bjma/1358864555


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