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arXiv · 1711.08985

A local-to-global boundedness argument and Fourier integral operators

Michael Ruzhansky·Mitsuru Sugimoto
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Abstract

We give a criterion for the global boundedness of integral operators which are known to be locally bounded. As an application, we discuss the global $L^p$-boundedness for a class of Fourier integral operators. While the local $L^p$-boundedness of Fourier integral operators is known from the work of Seeger, Sogge and Stein, not so many results are available for the global boundedness on $L^p({\mathbb R}^n)$. We give several natural sufficient conditions for them.

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Michael Ruzhansky, Mitsuru Sugimoto. 2017-11-24. A local-to-global boundedness argument and Fourier integral operators. https://arxiv.org/abs/1711.08985

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