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MIXED NORM INEQUALITIES FOR SOME DIRECTIONAL MAXIMAL OPERATORS

Part of: Harmonic analysis in several variables Integral, integro-differential, and pseudodifferential operators

Published online by Cambridge University Press:  16 February 2012

DAH-CHIN LUOR
DAH-CHIN LUOR*
Affiliation:
Department of Applied Mathematics, I-Shou University, Dashu District, Kaohsiung City 84001, Taiwan (email: [email protected])
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Abstract

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Mixed norm inequalities for directional operators are closely related to the boundedness problems of several important operators in harmonic analysis. In this paper we prove weighted inequalities for some one-dimensional one-sided maximal functions. Then by applying these results, we establish mixed norm inequalities for directional maximal operators which are defined from these one-dimensional maximal functions. We also estimate the constants in these inequalities.

Keywords

weighted inequalitiesmixed norm inequalitiesdirectional maximal operatorsmaximal functions

MSC classification

Secondary: 42B25: Maximal functions, Littlewood-Paley theory 47G10: Integral operators
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 3 , December 2012 , pp. 448 - 455
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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