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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the $ L\sp{2}$-boundedness of pseudo-differential operators


Author: A. G. Childs
Journal: Proc. Amer. Math. Soc. 61 (1976), 252-254
MSC: Primary 47G05; Secondary 35S05
MathSciNet review: 0442755
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Abstract: A. P. Calderón and R. Vaillancourt have established $ {L^2}$-boundedness in case the symbol has bounded partial derivatives to order $ 3$ in any variable. H. O. Cordes has proved $ {L^2}$-boundedness if this order is $ 1$. It is shown here that it suffices for the symbol to satisfy a uniform Hölder continuity condition of order $ \tfrac{1} {2} + \delta ,\;\delta > 0$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0442755-2
PII: S 0002-9939(1976)0442755-2
Keywords: $ {L^2}$-boundedness, pseudo-differential operator, symbol, Fourier transform, modified Hankel function
Article copyright: © Copyright 1976 American Mathematical Society