Orthogonality Principle for Bilinear Littlewood-Paley Decompositions

摘要

We explore Littlewood-Paley like decompositions of bilinear Fourier multipliers. Grafakos and Li (Am. J. Math. 128(1):91-119 2006) showed that a bilinear symbol supported in an angle in the positive quadrant is bounded from into if its restrictions to dyadic annuli are bounded bilinear multipliers in the local case , , . We show that this range of indices is sharp and also discuss similar results for multipliers supported near axis and negative diagonal.