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Uniform estimates on multi-linear operators with modulation symmetry

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Abstract

In a previous paper [20] in this series, we gaveL p estimates for multi-linear operators given by multipliers which are singular on a non-degenerate subspace of some dimensionk. In this paper, we give uniform estimates when the subspace approaches a degenerate region in the casek = 1, and when all the exponentsp are between 2 and ∞. In particular, we recover the non-endpoint uniform estimates for the bilinear Hubert transform in [12].

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Authors and Affiliations

  1. Department of Mathematics, UCLA, 90095-1555, Los Angeles, CA, USA

    Camil Muscalu, Terence Tao & Christoph Thiele

Authors
  1. Camil Muscalu
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  2. Terence Tao
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  3. Christoph Thiele
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Correspondence to Camil Muscalu.

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Dedicated to Tom Wolff

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Muscalu, C., Tao, T. & Thiele, C. Uniform estimates on multi-linear operators with modulation symmetry. J. Anal. Math. 88, 255–309 (2002). https://doi.org/10.1007/BF02786579

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  • DOI: https://doi.org/10.1007/BF02786579

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