GLOBAL $L^2$-BOUNDEDNESS THEOREMS FOR A CLASS OF FOURIER INTEGRAL OPERATORS AND THEIR APPLICATION (Recent Trends in Microlocal Analysis)

By Michael Ruzhansky, Mitsuru Sugimoto. 2005

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View Paper: https://www.semanticscholar.org/paper/a9ab189a00f28c460a37f38ad76cb93175266f91

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Citations in the corpus

Global $L^p$ continuity of Fourier integral operators (2009, methodology): “nt to assume the boundedness (2.3) since it fails for non-mixed derivatives (i.e. when α= 0 or β= 0), e.g. in applications to smoothing estimates for dispersive equations. For example, it is shown in [26, 27] that for canonical transforms appearing there condition (2.3) fails, but it is also shown t”
Quantization of Pseudo-differential Operators on the Torus (2008, result): “Therefore, this theorem relaxes assumptions on the behaviour with respect to the dual variable, compared, for example, with the corresponding result by Ruzhansky and Sugimoto [ 20 ].”
On the Fourier analysis of operators on the torus (2006, background): “Theorem 5.2 is the discrete version of the global boundedness theorem in [ 12 ].”
Changes of variables in modulation and Wiener amalgam spaces (2008, background): “rm side (e.g. [8]). Regularity properties of canonical transforms are important for various applications, for example in recent applications to global smoothing problems for evolution equations (e.g. [23, 24]). Since the Fourier image of a modulation space is a Wiener amalgam space it is natural to ”
On the boundedness of Fourier integral operators on (2010, background): “These results essentially extend the local Lp results of Seeger, Sogge and Stein [21] as well as global L2 results of Asada and Fujiwara [1], and Ruzhansky and Sugimoto [17], to the global setting of Lp(Rn), and the main concern of this paper is the global loss of weight in the Lp-boundedness.”
On the global boundedness of Fourier integral operators (2008, methodology): “(cf. [24]) that the composition A∗Ais a pseudodifferential operator with symbol in SG0,0; therefore it is continuous on L2(Rd) (e.g., by [25, Theorem 18.1.11]). So Ais. This result was generalized in [37] to FIOs with phases satisfying weaker symbol estimates. ON THE GLOBAL BOUNDEDNESS OF FOURIER IN”