## Abstract

Let P and Q be two polynomials without constant term. Assume that the operator B _{P,Q} ( f ,g)(x) = f (x-P(t))g(x-Q(t)) dt /t is bounded from L ^{p1} ×L ^{p2} into L ^{r} , p1, p2 ∈ (1,∞), 1/ p1 + 1/ p2 = 1/r . It is proved that if P′ (t) > 0 for all t ≠= 0, then r ≥ d/ d+1 . Here d is the correlation degree of P and Q which is defined as the largest multiplicity of non-zero real roots of P′ -Q′.

Original language | English (US) |
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Pages (from-to) | 151-156 |

Number of pages | 6 |

Journal | Mathematical Inequalities and Applications |

Volume | 22 |

DOIs | |

State | Published - Jan 2019 |

### Funding

This research is supported by LTS grant DO 0052. The author would also like to thank Prof. Xiaochun Li for helpful discussions on related topics.

## Keywords

- Bilinear hilbert transform
- Boundedness
- Correlation degree
- Full range

## ASJC Scopus subject areas

- General Mathematics
- Applied Mathematics