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

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

2000-08-02

arxiv.org/abs/math/0008019v1

Ann. of Math. (2) 151 (2000), no. 1, 35-57

Mathematics

Classical Analysis and ODEs

23 pages

Scientific paper

The bilinear maximal operator defined below maps $L^p\times L^q$ into $L^r$
provided $1Mfg(x)=\sup_{t>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 Calder\'on.

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