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Multi-Parameter Maximal Operators Associated with Finite Measures and Arbitrary Sets of Parameters

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Abstract

In this paper we examine various singular maximal operators, extending the class of operators which have been studied extensively in the past. It extends work that has been done in the one-parameter to the multi-parameter setting. We obtain the \(L^p\)-boundedness properties of the multi-parameter maximal operators associated with finite measures and arbitrary sets of parameters by assuming some Fourier decay and a certain geometric condition.

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Authors and Affiliations

  1. Department of Mathematics, Korea University, Seoul, 136-701, South Korea

    Yaryong Heo 

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  1. Yaryong Heo 
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Correspondence to Yaryong Heo .

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This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology NRF-2015R1A1A1A05001304.

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Heo , Y. Multi-Parameter Maximal Operators Associated with Finite Measures and Arbitrary Sets of Parameters. Integr. Equ. Oper. Theory 86, 185–208 (2016). https://doi.org/10.1007/s00020-016-2328-8

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  • DOI: https://doi.org/10.1007/s00020-016-2328-8

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