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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the boundedness of pseudo differential operators in the class $ L\sp{m}\sb{\rho }{}\sb{,1}.$


Author: Luigi Rodino
Journal: Proc. Amer. Math. Soc. 58 (1976), 211-215
MSC: Primary 47G05; Secondary 35S05
DOI: https://doi.org/10.1090/S0002-9939-1976-0410480-X
MathSciNet review: 0410480
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Abstract: We prove that every pseudo differential operator in the class $ L_{\rho ,1}^m,0 \leq \rho \leq 1$, is bounded in $ {L^2}({{\mathbf{R}}^n})$ if and only if $ m < n(\rho - 1)/2$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0410480-X
Keywords: Pseudo differential operator, symbol of a pseudo differential operator, class $ S_{\rho ,\delta }^m$, class $ L_{\rho ,\delta }^m$
Article copyright: © Copyright 1976 American Mathematical Society