On the \(L^ 2\) boundedness theorem of non-homogeneous Fourier integral operators in \(R^ n\)
type: Item
instance of: scholarly article
title: On the \(L^ 2\) boundedness theorem of non-homogeneous Fourier integral operators in \(R^ n\)
zbMATH Open document ID: 0566.35097
author: K. Asada
published in: Kodai Mathematical Journal
publication date: 1984-01-01T00:00:00Z
review text: Verf. betrachtet Fourierintegraloperatoren \[ Af(x)=(2\pi)^{- n}\int_{R^ n}e^{iS(x,\xi)}a(x,\xi)\hat f(\xi)d\xi, \] mit \(| \partial_ x^{\alpha}\partial^{\beta}_{\xi}a(x,\xi)| \leq C_{\alpha \beta}\lambda (\xi)^{\mu +| \alpha | -| \beta |}\) und \(| \partial_ x^{\alpha}\partial^{\beta}_{\xi}S(x,\xi)| \leq C_{\alpha \beta}\lambda (\xi)^{| \alpha | -| \beta |}.\) Verf. gibt eine weite Klasse von Gewichtsfunktionen \(\lambda\) (\(\xi)\) an, unter denen die obigen Operatoren \(A: L^ 2\to L^ 2\) beschränkt sind.
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 3903206
zbMATH Keywords: Fourier integral operator
zbMATH Keywords: weight function
zbMATH Keywords: boundedness
reviewed by: Josef Wloka
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138036911
OpenAlex ID: W1992229724
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DOI: 10.2996/KMJ/1138036911
description: scientific article; zbMATH DE number 3903206