The bilinear maximal functions map into Lp for 2 / 3 < p ≤ 1

@inproceedings{Lacey2000TheBM,
  title={The bilinear maximal functions map into Lp for 2 / 3 < p ≤ 1},
  author={Michael T. Lacey},
  year={2000}
}
The bilinear maximal operator defined below maps Lp × Lq into Lr provided 1 < p, q <∞, 1/p+ 1/q = 1/r and 2/3 < r ≤ 1. Mfg(x) = sup t>0 1 2t ∫ 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 Calderón. 1. Principal results In 1964 Alberto Calderón defined a family of maximal operators by Mfg(x) = sup t>0 1 2t ∫ t −t |f(x− αy)g(x− y)| dy, α 6= 0, 1 which have come to be known as bisublinear maximal functions. He… CONTINUE READING
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