The boundedness of bilinear Fourier integral operators on $L^2\times L^2$

[1] H. Abels, Pseudodifferential and singular integral operators. An introduction with applications, de Gruyter, Berlin,
2012.
[2] OF. Aid and A. Senoussaoui, The boundedness of h-admissible Fourier integral operators on Bessel potential
spaces, Turk. J. Math. 43 (2019), no. 5, 2125 – 2141.
[3] O.F. Aid and A. Senoussaoui, Hs
-Boundeness of a class of a Fourier integral operators, Math. Slovaca 71 (2021),
no. 4, 889–902.
[4] K. Asada and D. Fujiwara, On some oscillatory transformations in L
2
(R
n), Japanese J. Math. 4 (1978), no. 2,
299–361.
[5] A. B´enyi and T. Oh, ´ On a class of bilinear pseudodifferential operators, J. Funct. Spaces Appl. 2013 (2013), 1–5.
[6] A. B´enyi and K.A. Okoudjou, ´ Bilinear pseudodifferential operators on modulation spaces, J. Fourier Anal. Appl.
10 (2004), 301–313.
[7] A. B´enyi and K.A. Okoudjou, ´ Modulation spaces estimates for multilinear pseudodifferential operators, Stud.
Math. 172 (2006), 169–180.
[8] A. B´enyi, K. Groechenig, C. Heil and K. Okoudjou, ´ Modulation spaces and a class of bounded multilinear pseudodifferential operators, J. Oper. Theory 54 (2005), 389–401.
[9] A. B´enyi, D. Maldonado, V. Naibo and R.H. Torres, ´ On the H¨ormander classes of bilinear pseudodifferential
operators, Integr. Equ. Oper. Theory 67 (2010), 341–364.
[10] M. Cappiello and J. Toft, Pseudo-differential operators in a Gelfand–Shilov setting, Math. Nachr. 290 (2017),
738–755.
[11] R.R. Coifman and Y. Meyer, On commutators of singular integrals and bilinear singular integrals, Trans. Amer.
Math. Soc. 212 (1975), 315–331.[12] R.R. Coifman and Y. Meyer, Commutateurs d’int´egrales singuli`eres et op´erateurs multilin´eaires, Ann. Inst. Fourier
(Grenoble) 28 (1978), 177–202.
[13] R.R. Coifman and Y. Meyer, Au del`a des op´erateurs pseudo-diff´erentiels, Ast´erisque, No. 57, Soci´et´e
Math´ematique de France, 1979.
[14] E. Cordero and KA. Okoudjou, Multilinear localization operators, J. Math. Anal. Appl. 325 (2007), 1103–1116.
[15] L. Grafakos and R.H. Torres, Multilinear Calder´on–Zygmund theory, Adv. Math. 165 (2002), 124–164.
[16] L. Grafakos, Modern fourier analysis, Third edition, Springer, New York, 2014.
[17] N. Hamada, N. Shida and N. Tomita, On the ranges of bilinear pseudo-differential operators of S0,0-type on
L
2 × L
2
, J. Funct. Anal. 280 (2021), no. 3, 108826.
[18] T. Kato, Bilinear pseudo-differential operators with exotic class symbols of limited smoothness, J. Fourier Anal.
Appl. 27 (2021), 1–56.
[19] K. Koezuka and N. Tomita, Bilinear pseudo-differential operators with symbols in BSm
1,1 on Triebel–Lizorkin
spaces, J. Fourier Anal. Appl. 24 (2018) 309–319.
[20] S. Molahajloo, K.A. Okoudjou and G.E. Pfander, Boundedness of multilinear pseudodifferential operators on
modulation spaces, J. Fourier Anal. Appl. 22 (2016), 1381–1415.
[21] S. Rodr´ıguez-L´opez, D. Rule and W. Staubach, Global boundedness of a class of multilinear Fourier integral
operators, Forum Math. Sigma 9 (2021), 1–45.