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$ \mathrm{L}^p$ estimates for a singular entangled quadrilinear form

Author: Polona Durcik
Journal: Trans. Amer. Math. Soc. 369 (2017), 6935-6951
MSC (2010): Primary 42B15; Secondary 42B20
Published electronically: March 30, 2017
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Abstract: We prove $ \mathrm {L}^p$ estimates for a continuous version of a dyadic quadrilinear form introduced by V. Kovač (2012). This improves the range of exponents from the prequel of the present paper.

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  • [1] Frédéric Bernicot, Fiber-wise Calderón-Zygmund decomposition and application to a bi-dimensional paraproduct, Illinois J. Math. 56 (2012), no. 2, 415-422. MR 3161332
  • [2] Ciprian Demeter and Christoph Thiele, On the two-dimensional bilinear Hilbert transform, Amer. J. Math. 132 (2010), no. 1, 201-256. MR 2597511,
  • [3] Polona Durcik, An $ L^4$ estimate for a singular entangled quadrilinear form, Math. Res. Lett. 22 (2015), no. 5, 1317-1332. MR 3488377,
  • [4] Roger L. Jones, Andreas Seeger, and James Wright, Strong variational and jump inequalities in harmonic analysis, Trans. Amer. Math. Soc. 360 (2008), no. 12, 6711-6742. MR 2434308,
  • [5] Vjekoslav Kovač, Bellman function technique for multilinear estimates and an application to generalized paraproducts, Indiana Univ. Math. J. 60 (2011), no. 3, 813-846. MR 2985857,
  • [6] Vjekoslav Kovač, Boundedness of the twisted paraproduct, Rev. Mat. Iberoam. 28 (2012), no. 4, 1143-1164. MR 2990138,
  • [7] Camil Muscalu, Terence Tao, and Christoph Thiele, Uniform estimates on multi-linear operators with modulation symmetry, J. Anal. Math. 88 (2002), 255-309. Dedicated to the memory of Tom Wolff. MR 1979774,
  • [8] Elias M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, with the assistance of Timothy S. Murphy, Monographs in Harmonic Analysis, III, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993. MR 1232192
  • [9] Christoph Martin Thiele, Time-frequency analysis in the discrete phase plane, with a section written with Lars Villemoes, Topics in analysis and its applications, World Sci. Publ., River Edge, NJ, 2000, pp. 99-152. MR 1882552,
  • [10] Christoph Thiele, Wave packet analysis, CBMS Regional Conference Series in Mathematics, vol. 105, published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2006. MR 2199086

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Additional Information

Polona Durcik
Affiliation: Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany

Received by editor(s): July 5, 2015
Received by editor(s) in revised form: October 1, 2015
Published electronically: March 30, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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