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

• 成果类型: Article
• 署名作者: Lacey, MT
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/121111
• 发表日期: 2000
• 页码: 35-57
• 关键词: hilbert transform

摘要

The bilinear maximal operator defined below maps L-p x L-q into L-r provided 1 < p, q < infinity, 1/p + 1/q = 1/r and 2/3 < r less than or equal to 1. Mfg(x) = sup(t>0) 1/2t integral(-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.