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) |
|---|---|
| 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