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Weighted estimates for the multisublinear maximal function

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Abstract

A formulation of the Carleson embedding theorem in the multilinear setting is proved which allows obtaining a multilinear analogue of Sawyer’s two weight theorem for the multisublinear maximal function \(\mathcal{M }\) introduced by Lerner et al. (Adv Math 220:1222–1264, 2009). A multilinear version of the \(B_p\) theorem from Hytönen and Pérez (Anal PDE, 2013) is also obtained and a mixed \(A_{\overrightarrow{ P}}-W_{\overrightarrow{ P}}^{\infty }\) bound for \(\mathcal{M }\) is proved as well.

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Acknowledgments

This paper was completed while W. Chen was at the Institute of Mathematics of the University of Seville (I.M.U.S.), Spain. He would like to express his gratitude for the hospitality received there. The authors would like to thank Prof. Carlos Pérez for his advice and support and his helpful remarks. W. Chen is supported by the National Natural Science Foundation of China (Grant No. 11101353), the Natural Science Foundation of Jiangsu Education Committee (Grant No. 11KJB110018) and the Natural Science Foundation of Jiangsu Province (Grant No. BK2012682). W. Damián is supported by Junta de Andalucía (Grant No. P09-FQM-4745).

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Authors and Affiliations

  1. School of Mathematical Sciences, Yangzhou University, Yangzhou, 225002, China

    Wei Chen

  2. Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, 41080 , Seville, Spain

    Wendolín Damián

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  1. Wei Chen
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  2. Wendolín Damián
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Correspondence to Wendolín Damián.

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Chen, W., Damián, W. Weighted estimates for the multisublinear maximal function. Rend. Circ. Mat. Palermo 62, 379–391 (2013). https://doi.org/10.1007/s12215-013-0131-9

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  • DOI: https://doi.org/10.1007/s12215-013-0131-9

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