An extension on Trilinear Hilbert transform

Abstract

The Trilinear Hilbert transform H: Lp x Lq x A -> Lr is extended to DLp x DLq x DA -> DLr -> as a continuous mapping.

Inversion theorem for bilinear Hilbert transform

“…Since p 3 ≤ p 1 , it follows that f ∈ L p 3 loc . By Lemma 2.1, J → 0 as r → 0 and the Lemma is proved because K → 0 as r → 0.…”

“…q 1 , (with suitable parameters) as a hypocontinuous, respectively, continuous mapping. The trilinear Hilbert transform on D L p × D L q × D A → D L r is studied in [3]. This analysis is based on [7].…”