Lacey, Michael; Thiele, Christoph \(L^p\) estimates for the bilinear Hilbert transform. (English) Zbl 0946.44001 Proc. Natl. Acad. Sci. USA 94, No. 1, 33-35 (1997). Summary: For the bilinear Hilbert transform given by \[ Hfg(x)=\text{p.v. }\int f(x-y)g(x+y){dy\over y}, \] we announce the inequality \(\|H fg\|_{p_3}\leq K_{p_1,p_2}\|f\|_{p_1}\|g\|_{p_2}\), provided \(2<p_1, p_2<\infty\), \(1/p_3=1/p_1+1/p_2\) and \(1<p_3<2\). Cited in 15 Documents MSC: 44A15 Special integral transforms (Legendre, Hilbert, etc.) 47A30 Norms (inequalities, more than one norm, etc.) of linear operators Keywords:norms; \(L^p\) estimates; bilinear Hilbert transform; inequality PDF BibTeX XML Cite \textit{M. Lacey} and \textit{C. Thiele}, Proc. Natl. Acad. Sci. USA 94, No. 1, 33--35 (1997; Zbl 0946.44001) Full Text: DOI OpenURL References: [1] Calderon, PNAS 53 (5) pp 1092– (1965) · Zbl 0151.16901 [2] ACTA MATH 116 pp 135– (1966) · Zbl 0144.06402 [3] ANN MATH 98 pp 551– (1973) · Zbl 0268.42009 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.