Local estimates and global continuities in Lebesgue spaces for bilinear operators

Details Local estimates and global continuities in Lebesgue spaces for bilinear operators Local estimates and global continuities in Lebesgue spaces for bilinear operators

2008-01-26

arxiv.org/abs/0801.4088v3

Mathematics

Functional Analysis

37 pages

Scientific paper

In this paper, we first prove some local estimates for bilinear operators (closely related to the bilinear Hilbert transform and similar singular operators) with truncated symbol. Such estimates, in accordance with the Heisenberg uncertainty principle correspond to a description of ``off-diagonal'' decay. In addition they allow us to prove global continuities in Lebesgue spaces for bilinear operators with spatial dependent symbol.

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