Criterion on Lp1×Lp2→Lq-Boundedness for Oscillatory Bilinear Hilbert Transform. (25th February 2014)

• Record Type: Journal Article
• Authors: Shi, Zuoshunhua; Yan, Dunyan
• Other Names: Fan Dashan Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-02-25
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/712051
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We investigate the bilinear Hilbert transform with oscillatory factors and the truncated bilinear Hilbert transform. The main result is that theL p 1 × L p 2 → L q -boundedness of the two operators is equivalent with1 ≤ p 1, p 2 < ∞, and1 / q = 1 / p 1 + 1 / p 2 . In addition, we also discuss the boundedness of a variant operator of bilinear Hilbert transform with a nontrivial polynomial phase.