On the bilinear Hilbert transform along two polynomials

Dong Dong*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We prove that the bilinear Hilbert transform along two polynomials BP,Q(f, g)(x) = R f(x − P(t))g(x − Q(t)) dt t is bounded from Lp × Lq to Lr for a large range of (p, q, r), as long as the polynomials P and Q have distinct leading and trailing degrees. The same boundedness property holds for the corresponding bilinear maximal function MP,Q(f, g)(x) = sup ε> 0 2 1 ε ε ε |f(x − P(t))g(x − Q(t))|dt.

Original languageEnglish (US)
Pages (from-to)4245-4258
Number of pages14
JournalProceedings of the American Mathematical Society
Volume147
Issue number10
DOIs
StatePublished - 2019

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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