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Global boundedness of a class of multilinear Fourier integral operators

Published online by Cambridge University Press:  22 February 2021

Salvador Rodríguez-López
Affiliation:
Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden; E-mail: s.rodriguez-lopez@math.su.se
David Rule
Affiliation:
Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden; E-mail: david.rule@liu.se
Wolfgang Staubach
Affiliation:
Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden; E-mail: s.rodriguez-lopez@math.su.se Department of Mathematics, Uppsala University, SE-751 06 Uppsala, Sweden; E-mail: wulf@math.uu.se

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.

Type
Analysis
Creative Commons
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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