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On the Hardy-Littlewood maximal function for the cube

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Abstract

It is shown that the Hardy-Littlewood maximal function associated to the cube in ℝn obeys dimensional free bounds in L p for p > 1. Earlier work only covered the range p > \(\frac{3}{2}\).

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Authors and Affiliations

  1. School of Mathematics, Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ, 08540, USA

    Jean Bourgain

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  1. Jean Bourgain
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Correspondence to Jean Bourgain.

Additional information

Dedicated to J. Lindenstrauss

The research was partially supported by NSF grants DMS-0808042 and DMS-0835373.

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Bourgain, J. On the Hardy-Littlewood maximal function for the cube. Isr. J. Math. 203, 275–293 (2014). https://doi.org/10.1007/s11856-014-1059-2

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  • DOI: https://doi.org/10.1007/s11856-014-1059-2

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