L(p) estimates for the bilinear Hilbert transform.
For the bilinear Hilbert transform given by: H fg(x) = p.v.integral f(x - y)g(x + y) dyy, we announce the inequality parallel H fg parallel (p(3) ) </= K(p(1) ) (,p(2) ) parallel f parallel (p(1) ) parallel g parallel (p(2) ), provided 2 < p(1), p(2) < infinity, 1/p(3) = 1/p(1) + 1/p(2) and 1 < p(3) < 2.
Lacey
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M
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA.
Thiele
C
C