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

Durcik, Polona

doi:10.1090/tran/6850

$\mathrm {L}^p$ estimates for a singular entangled quadrilinear form
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Trans. Amer. Math. Soc. 369 (2017), 6935-6951 Request permission

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.

References

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
Ciprian Demeter and Christoph Thiele, On the two-dimensional bilinear Hilbert transform, Amer. J. Math. 132 (2010), no. 1, 201–256. MR 2597511, DOI 10.1353/ajm.0.0101
Polona Durcik, An $L^4$ estimate for a singular entangled quadrilinear form, Math. Res. Lett. 22 (2015), no. 5, 1317–1332. MR 3488377, DOI 10.4310/MRL.2015.v22.n5.a3
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, DOI 10.1090/S0002-9947-08-04538-8
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, DOI 10.1512/iumj.2011.60.4784
Vjekoslav Kovač, Boundedness of the twisted paraproduct, Rev. Mat. Iberoam. 28 (2012), no. 4, 1143–1164. MR 2990138, DOI 10.4171/RMI/707
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, DOI 10.1007/BF02786579
Elias M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993. With the assistance of Timothy S. Murphy; Monographs in Harmonic Analysis, III. MR 1232192
Christoph Martin Thiele, Time-frequency analysis in the discrete phase plane, Topics in analysis and its applications, World Sci. Publ., River Edge, NJ, 2000, pp. 99–152. With a section written with Lars Villemoes. MR 1882552, DOI 10.1142/9789812813305_{0}003
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, DOI 10.1090/cbms/105