scholarly journals Mapping Properties of Integral Operators of Levy Type

2005 ◽  
Vol 12 (2) ◽  
pp. 377-387
Author(s):  
Thomas Runst ◽  
Abdellah Youssfi
Keyword(s):  
Sobolev Spaces ◽  
Special Class ◽  
Integral Operators ◽  
Generalized Sobolev Spaces

Abstract We study the boundedness and compactness of a special class of integral operators defined on generalized Sobolev spaces.

scholarly journals The boundedness of a class of semiclassical Fourier integral operators on Sobolev space $H^{s}$

2021 ◽  
Vol 56 (1) ◽  
pp. 61-66
Author(s):  
O. F. Aid ◽  
A. Senoussaoui
Keyword(s):  
Sobolev Space ◽  
Sobolev Spaces ◽  
Integral Operators ◽  
Fourier Integral ◽  
Schwartz Space ◽  
Background Information ◽  
Fourier Integral Operators ◽  
Phase Functions

We introduce the relevant background information thatwill be used throughout the paper.Following that, we will go over some fundamental concepts from thetheory of a particular class of semiclassical Fourier integraloperators (symbols and phase functions), which will serve as thestarting point for our main goal. Furthermore, these integral operators turn out to be bounded on$S\left(\mathbb{R}^{n}\right)$ the space of rapidly decreasingfunctions (or Schwartz space) and its dual$S^{\prime}\left(\mathbb{R}^{n}\right)$ the space of temperatedistributions. Moreover, we will give a brief introduction about$H^s(\mathbb{R}^n)$ Sobolev space (with $s\in\mathbb{R}$).Results about the composition of semiclassical Fourier integraloperators with its $L^{2}$-adjoint are proved. These allow to obtainresults about the boundedness on the Sobolev spaces$H^s(\mathbb{R}^n)$.

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