scholarly journals Global boundedness of a class of multilinear Fourier integral operators

2021 ◽  
Vol 9 ◽  
Author(s):  
Salvador Rodríguez-López ◽  
David Rule ◽  
Wolfgang Staubach
Keyword(s):  
Wave Equations ◽  
Global Regularity ◽  
Integral Operators ◽  
Fourier Integral ◽  
Nonlinear Wave Equations ◽  
Fourier Integral Operators ◽  
Product Spaces ◽  
Local Hardy Space ◽  
Global Boundedness ◽  
Suitable Product

Abstract We establish the global regularity of multilinear Fourier integral operators that are associated to nonlinear wave equations on products of $L^p$ spaces by proving endpoint boundedness on suitable product spaces containing combinations of the local Hardy space, the local BMO and the $L^2$ spaces.

scholarly journals On the global boundedness of Fourier integral operators

2010 ◽  
Vol 38 (4) ◽  
pp. 373-398 ◽  
Author(s):  
Elena Cordero ◽  
Fabio Nicola ◽  
Luigi Rodino
Keyword(s):  
Integral Operators ◽  
Fourier Integral ◽  
Fourier Integral Operators ◽  
Global Boundedness

Square function inequality for a class of Fourier integral operators satisfying cinematic curvature conditions

2020 ◽  
Vol 32 (6) ◽  
pp. 1375-1394
Author(s):  
Chuanwei Gao ◽  
Changxing Miao ◽  
Jianwei-Urbain Yang
Keyword(s):  
Variable Coefficient ◽  
Wave Equations ◽  
Integral Operators ◽  
Oscillatory Integral ◽  
Fourier Integral ◽  
Acta Math ◽  
Fourier Integral Operators ◽  
Square Function ◽  
Local Smoothing ◽  
Smoothing Estimate

AbstractIn this paper, we establish an improved variable coefficient version of the square function inequality, by which the local smoothing estimate {L^{p}_{\alpha}\to L^{p}} for the Fourier integral operators satisfying cinematic curvature condition is further improved. In particular, we establish almost sharp results for {2<p\leqslant 3} and push forward the estimate for the critical point {p=4}. As a consequence, the local smoothing estimate for the wave equation on the manifold is refined. We generalize the results in [S. Lee and A. Vargas, On the cone multiplier in \mathbb{R}^{3}, J. Funct. Anal. 263 2012, 4, 925–940; J. Lee, A trilinear approach to square function and local smoothing estimates for the wave operator, preprint 2018, https://arxiv.org/abs/1607.08426v5] to its variable coefficient counterpart. The main ingredients in the argument includes multilinear oscillatory integral estimate [J. Bennett, A. Carbery and T. Tao, On the multilinear restriction and Kakeya conjectures, Acta Math. 196 2006, 2, 261–302] and decoupling inequality [D. Beltran, J. Hickman and C. D. Sogge, Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds, Anal. PDE 13 2020, 2, 403–433].

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