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Maximal operators associated with bilinear multipliers of limited decay

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Abstract

Results analogous to those proved by Rubio de Francia [28] are obtained for a class of maximal functions formed by dilations of bilinear multiplier operators of limited decay. We focus our attention on L2 × L2 → L1 estimates. We discuss two applications: the boundedness of the bilinear maximal Bochner-Riesz operator and of the bilinear spherical maximal operator. For the latter we improve the known results in [1] by reducing the dimension restriction from n ≥ 8 to n ≥ 4.

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Acknowledgments

The authors are indebted to the careful anonymous referees whose comments helped improve the presentation of this paper.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Missouri, Columbia, MO, 65211, USA

    Loukas Grafakos

  2. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China

    Danqing He

  3. Faculty of Mathematics and Physics, Charles University, Sokolovska 83, Praha 7, Czech Republic

    Petr Honzík

Authors
  1. Loukas Grafakos
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  2. Danqing He
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  3. Petr Honzík
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Corresponding author

Correspondence to Danqing He.

Additional information

The first author would like to acknowledge the support of the Simons Foundation and of the University of Missouri Research Board and Research Council.

The second author was supported by NNSF of China (No. 11701583), the Guangdong Natural Science Foundation (No. 2017A030310054), and the Fundamental Research Funds for the Central Universities (No. 17lgpy11).

The third author was supported by GAČR P201/18-07996S

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Grafakos, L., He, D. & Honzík, P. Maximal operators associated with bilinear multipliers of limited decay. JAMA 143, 231–251 (2021). https://doi.org/10.1007/s11854-021-0154-7

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  • DOI: https://doi.org/10.1007/s11854-021-0154-7

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