Bilinear maximal functions associated with surfaces

Chen, Jiecheng; Grafakos, Loukas; He, Danqing; Honzík, Petr; Slavíková, Lenka

doi:10.1090/proc/15792

Bilinear maximal functions associated with surfaces
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by Jiecheng Chen, Loukas Grafakos, Danqing He, Petr Honzík and Lenka Slavíková PDF

Proc. Amer. Math. Soc. 150 (2022), 1635-1639 Request permission

Abstract:

We obtain $L^2\times L^2\to L^1$ boundedness for bilinear maximal functions associated with general compact hypersurfaces. Our method is based on the strategy introduced by Barrionuevo et al. [Math. Res. Lett. 25 (2018), pp. 69–1388] and a new multiplier result established by Grafakos, He, and Slavíková [Math. Ann. 376 (2020), pp. 431–455].

References

J. Bourgain, Averages in the plane over convex curves and maximal operators, J. Analyse Math. 47 (1986), 69–85. MR 874045, DOI 10.1007/BF02792533
J. A. Barrionuevo, Loukas Grafakos, Danqing He, Petr Honzík, and Lucas Oliveira, Bilinear spherical maximal function, Math. Res. Lett. 25 (2018), no. 5, 1369–1388. MR 3917731, DOI 10.4310/MRL.2018.v25.n5.a1
Dan-Andrei Geba, Allan Greenleaf, Alex Iosevich, Eyvindur Palsson, and Eric Sawyer, Restricted convolution inequalities, multilinear operators and applications, Math. Res. Lett. 20 (2013), no. 4, 675–694. MR 3188026, DOI 10.4310/MRL.2013.v20.n4.a6
Javier Duoandikoetxea and José L. Rubio de Francia, Maximal and singular integral operators via Fourier transform estimates, Invent. Math. 84 (1986), no. 3, 541–561. MR 837527, DOI 10.1007/BF01388746
Loukas Grafakos, Danqing He, and Petr Honzík, Rough bilinear singular integrals, Adv. Math. 326 (2018), 54–78. MR 3758426, DOI 10.1016/j.aim.2017.12.013
Loukas Grafakos, Danqing He, and Petr Honzík, Maximal operators associated with bilinear multipliers of limited decay, J. Anal. Math. 143 (2021), no. 1, 231–251. MR 4299160, DOI 10.1007/s11854-021-0154-7
Loukas Grafakos, Danqing He, and Lenka Slavíková, $L^2\times L^2\to L^1$ boundedness criteria, Math. Ann. 376 (2020), no. 1-2, 431–455. MR 4055166, DOI 10.1007/s00208-018-1794-5
Allan Greenleaf, Principal curvature and harmonic analysis, Indiana Univ. Math. J. 30 (1981), no. 4, 519–537. MR 620265, DOI 10.1512/iumj.1981.30.30043
Lars Hörmander, The analysis of linear partial differential operators. I, 2nd ed., Springer Study Edition, Springer-Verlag, Berlin, 1990. Distribution theory and Fourier analysis. MR 1065136, DOI 10.1007/978-3-642-61497-2
Eunhee Jeong and Sanghyuk Lee, Maximal estimates for the bilinear spherical averages and the bilinear Bochner-Riesz operators, J. Funct. Anal. 279 (2020), no. 7, 108629, 29. MR 4103874, DOI 10.1016/j.jfa.2020.108629
Walter Littman, Fourier transforms of surface-carried measures and differentiability of surface averages, Bull. Amer. Math. Soc. 69 (1963), 766–770. MR 155146, DOI 10.1090/S0002-9904-1963-11025-3
José L. Rubio de Francia, Maximal functions and Fourier transforms, Duke Math. J. 53 (1986), no. 2, 395–404. MR 850542, DOI 10.1215/S0012-7094-86-05324-X
Elias M. Stein, Maximal functions. I. Spherical means, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 7, 2174–2175. MR 420116, DOI 10.1073/pnas.73.7.2174
Elias M. Stein and Stephen Wainger, Problems in harmonic analysis related to curvature, Bull. Amer. Math. Soc. 84 (1978), no. 6, 1239–1295. MR 508453, DOI 10.1090/S0002-9904-1978-14554-6