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.

中文翻译：

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与有限衰变双线性乘法器相关的最大算子

对于由有限衰减的双线性乘子算子的扩张形成的一类最大函数，获得了类似于Rubio de Francia [28]证明的结果。我们将注意力集中在L ² × L ² → L ¹估计上。我们讨论了两个应用：双线性最大Bochner-Riesz算子和双线性球形最大算子的有界性。对于后者，我们通过从减小尺寸限制改善[1]的已知结果Ñ ≥8至Ñ ≥4。