Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



On the $L^{2}$-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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $\tfrac {1} {2} + \delta ,\;\delta > 0$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47G05, 35S05

Retrieve articles in all journals with MSC: 47G05, 35S05

Additional Information

Keywords: <IMG WIDTH="28" HEIGHT="23" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${L^2}$">-boundedness, pseudo-differential operator, symbol, Fourier transform, modified Hankel function
Article copyright: © Copyright 1976 American Mathematical Society