Global L2-boundedness theorems for a class of Fourier integral operators
Michael Ruzhansky, Mitsuru Sugimoto
Abstract
The local L2-mapping property of Fourier integral operators has been established in Hörmander H and in Eskin E. In this paper, we treat the global L2-boundedness for a class of operators that appears naturally in many problems. As a consequence, we will improve known global results for several classes of pseudo-differential and Fourier integral operators, as well as extend previous results of Asada and Fujiwara AF or Kumano-go Ku. As an application, we show a global smoothing estimate to generalized Schrödinger equations which extends the results of Ben-Artzi and Devinatz BD, Walther Wa, and Wa2.
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