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arXiv · 1804.08537

Maximal operators associated with bilinear multipliers of limited decay

Loukas Grafakos·Danqing He·Petr Honzík
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Abstract

Results analogous to those proved by Rubio de Francia are obtained for a class of maximal functions formed by dilations of bilinear multiplier operators of limited decay. We focus our attention to $L^2\times L^2\to L^1$ 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 by reducing the dimension restriction from $n\ge 8$ to $n\ge 4$.

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Loukas Grafakos, Danqing He, Petr Honzík. 2018-04-23. Maximal operators associated with bilinear multipliers of limited decay. https://arxiv.org/abs/1804.08537

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