Abstract.
We prove L p estimates (Theorem 1.8) for the Walsh model of the ‘‘biest’’, a trilinear multiplier with singular symbol. The corresponding estimates for the Fourier model will be obtained in the sequel [11] biest of this paper.
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Christ, M., Kiselev, A.: WKB asymptotic behavior of almost all generalized eigenfunctions for one-dimensional Schrödinger operators with slowly decaying potentials. J. Funct. Anal. 179, 426–447 (2001)
Christ, M., Kiselev, A.: WKB and spectral analysis of one-dimensional Schrödinger operators with slowly varying potential. Comm. Math. Phys. 218, 245–262 (2001)
Fefferman C.: Pointwise convergence of Fourier series. Ann. of Math. 98(2), 551–571 (1973)
Gilbert J., Nahmod A.: Boundedness of bilinear operators with non-smooth symbols. Math. Res. Lett. 7, 767–778 (2000)
Grafakos L., Li, X.: Uniform bounds for the bilinear Hilbert transform I. Preprint 2000
Janson, S.: On interpolation of multilinear operators in Cwickel, Peetre, Sager and Wallin (Eds.), Function Spaces and Applications. Proceedings Lund 1986, Springer LNM 1302, 1988
Lacey M.: The bilinear Hilbert transform is pointwise finite. Rev. Mat. Iberoam. 13, 411–469 (1997)
Lacey M., Thiele C.: L p estimates on the bilinear Hilbert transform for 2 < p < ∞. Ann. Math. 146, 693–724 (1997)
Lacey M., Thiele C.: On Calderon’s conjecture. Ann. Math. 149, 475–196 (1999)
Muscalu C., Tao T., Thiele C.: Multi-linear operators given by singular symbols. J. Am. Math. Soc. 15, 469–496 (2002)
Muscalu C., Tao T., Thiele C.: L p estimates for the biest II. The Fourier case. To appear in Math. Ann.(DOI: 10.1007/s00208-003-0508-8)
Muscalu C., Tao T., Thiele C.: A counterexample to a multilinear endpoint question of Christ and Kiselev. Math. Res. Lett. 10, 237–246 (2003)
Thiele C.: Ph. D. Thesis, Yale University, 1995
Thiele C.: The quartile operator and pointwise convergence of Walsh series. Trans. Am. Math. Soc. 352, 5745–5766 (2000)
Thiele C.: On the Bilinear Hilbert transform. Universität Kiel, Habilitationsschrift 1998
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Muscalu, C., Tao, T. & Thiele, C. L p estimates for the biest I. The Walsh case. Math. Ann. 329, 401–426 (2004). https://doi.org/10.1007/s00208-004-0518-1
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DOI: https://doi.org/10.1007/s00208-004-0518-1