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# The Bilinear Maximal Functions Map into Lp for 2/3 < p ≤ 1

Michael T. Lacey
Annals of Mathematics
Second Series, Vol. 151, No. 1 (Jan., 2000), pp. 35-57
DOI: 10.2307/121111
Stable URL: http://www.jstor.org/stable/121111
Page Count: 23
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## Abstract

The bilinear maximal operator defined below maps L p× Lq into Lr provided 1 < p, q < ∞ , 1/p + 1/q = 1/r and 2/3 < r ≤ 1. M f g(x = $\underset t>0\to{\sup}\frac{1}{2t}\int_{-t}^{t}|f(x+y)g(x-y)|$ dy. In particular Mfg is integrable if f and g are square integrable, answering a conjecture posed by Alberto Calderon.

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