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The bilinear maximal functions map into L^p for 2/3 < p <= 1

Michael T. Lacey
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Abstract

The bilinear maximal operator defined below maps $L^p\times L^q$ into $L^r$ provided $1 0}\frac1{2t}\int_{-t}^t\abs{f(x+y)g(x-y)} dy.$$ In particular $Mfg$ is integrable\thinspace if $f$ and $g$ are square integrable, answering a conjecture posed by Alberto Calderón.

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Michael T. Lacey. 2000-08-02. The bilinear maximal functions map into L^p for 2/3 < p <= 1. https://arxiv.org/abs/math/0008019

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