Mathematics > Classical Analysis and ODEs
[Submitted on 23 Apr 2018 (v1), last revised 24 Apr 2018 (this version, v2)]
Title:Maximal operators associated with bilinear multipliers of limited decay
View PDFAbstract: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 $n\ge 4$.
Submission history
From: Danqing He [view email][v1] Mon, 23 Apr 2018 16:23:00 UTC (28 KB)
[v2] Tue, 24 Apr 2018 22:02:39 UTC (28 KB)
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